Obira Daniel Solar Dryer Computer Model Project

Gulu University Faculty of Agriculture and Environment Biosystems Engineering Department Fourth Year Engineering Project: A computer model to optimize the solar performance of a hybrid tunnel solar dryer. By Obira Daniel 08/U/953/BSE obiradaniel@gmail.com Lead Supervisor: Eng. Ebangu Ben Orari Assistant Supervisor: Professor Yun Sun Chol Student Signature: ___________ Date: ________ ACKNOWLEDGEMENT I would like to express my sincere gratitude and appreciation to my parents Mr. Obira Ignatius (R.I.P) and Mrs. Aujo Jane and my entire family for all they have done and are still doing for me, may God bless them. I would also like to thank my lead supervisor Eng. Ben Ebangu for giving me the project idea in the first place and for the technical and motivative support and ideas he gave to me along with the entire Biosystems Engineering Department and student body. A special vote of thanks goes to Professor Yun Sun Chol for all the technical and motivative support, recommendations, data and numerical solving techniques he shared with me despite his limited time. I would like to appreciate the work and effort of many scholars who laid a fundamental foundation in solar drying systems simulation, modeling and redesigning between 19851994 especially Prof. B.K Bala (Department of Farm Power and Machinery, Bangladesh Agricultural University), Prof. Serm Janjai (Department of Physics, Silpakorn University), Woods J.L and the scholars who also laid a foundation optimization of simulated solar drying systems like I.N. Simate for all their contribution towards solar drying modeling. I appreciate the work and effort of all my lecturers especially for the courses fundamental to the work presented here; Engineering Math, Computer graphics and CAD, Engineering and applied thermodynamics, Mechanics of fluids, Computer programming using MATLAB, Physical properties of biological materials, Renewable energy sources & utilization, Hydrology-climatology and modeling, Drying and air conditioning of agricultural products, Principles of food processing and preservation and lastly Engineering economy and operations research. Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 i DECLARATION I Obira Daniel, do declare to the best of my knowledge that the content presented in this project report is personally developed and has not been presented in any other institution, University and college of learning. Obira Daniel Signature: ___________ Date of Submission: _______________ APPROVAL This report is submitted in partial fulfillment of the requirements for the award of the degree of Bachelor of Science in Biosystems Engineering at Gulu University Lead Supervisor Eng. Ebangu Benedict Orari Head of Department Biosystems Engineering, Senior Lecturer of Electrical Engineering, renewable energy and control systems, Faculty of Agriculture and Environment, Gulu University ebangu.orari@gmail.com Signature………………………………. Date……………………………………. Assistant Supervisor Professor Yun Sun Chol Professor of fluid mechanics and thermodynamics, Faculty of Science and Department of Biosystems Engineering, Gulu University sunchol.yun40@gmail.com Signature………………………………. Date……………………………………. NOMENCLATURE Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 ii Letter symbols: A Area, (m2) C Specific Heat Capacity, (s.h.c, J/Kg K) db Distance between cover and galvanized bed, (m) dp Distance between cover and food product, (m) E Insolation, (W/m2) h Heat transfer coefficient, (W/m2K) hc Convective heat transfer coefficient, (W/m2K) HD Hydraulic Diameter, (m) hr Radiative heat transfer coefficient, (W/m2K) i Length interval notation equivalent to Δx K Drying constant k Thermo-conductivity, (W/mK). L Length, (m) Lv Latent heat of vaporization M Mass, (Kg) m moisture content (db or wb) Nu Nusselt Number Pr Prandtl Number Q Heat energy, (J) Qab Heat energy lost or gained by absorption or incident radiation, (J/s) Qc Heat energy lost or gained by convection, (J/s) Qcd Heat energy lost or gained by conduction, (J/s) Qr Heat energy lost or gained by radiation, (J/s) Ra Universal gas constant for air, Kgm2/s2kgK Ra Rayleigh Number Re Reynolds Number T Temperature, ( K or 0C) Va Air velocity in dryer, (m/s) vw Ambient Air/wind velocity, (m/s) w Humidity ratio, (Kg of moisture/Kg of dry air) W width of the chamber, (m) X Distance along the horizontal axis of the dryer, (m) z Thickness, (m). Subscripts: a Air inside the chamber (airflow) Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 iii am Ambient b Absorber(drying bed) c Cover dc Drying Chamber e Equilibrium f Final hc Heating chamber i Initial p Product py Papyrus mat (insulation) sk Sky v Water vapor w Water Greek letters µ Dynamic viscosity of air, (Pa.s) α Absorbance β Void bed fraction for product ε Emittance, Efficiency Angle of tilt to the horizontal of a given chamber, (0) σ Stefan-Boltzmann constant, (W/m2K4) Transmittance Reflectance Density, (Kg/m3) Angle of horizontal inclination of the cover, (0) Values of Constants g 9.81m/s2 Ra 287.07 Kgm2/s2KgK αb 0.74 αc 0.1 αp 0.8 εb 0.9,0.23 εc 0.6 εp 0.9 σ b 0.1,0.25 Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 iv p 0.2 2.80 for heating chamber and first two drying meshes, 00 for the 3rd drying mesh and 70 for the remaining drying chamber 0.8 4.90 Abbreviations and acronyms; ANN Artificial Neural Network ANSI American National Standards Institute ASABE American Society of Agricultural and Biological Engineers ASAE American Society of Agricultural Engineers CUDA Compute Unified Device Architecture DC Direct Current FORTRAN Formula Translator GPGPU General Purpose computing on Graphics Processing Units MATLAB Matrix Laboratory MC Moisture Content me Equilibrium Moisture content MSI Moisture Sorption Isotherm NN Neural Network PV Photovoltaic RGB Red Blue Green RMSE Root Mean Square Error s.h.c Specific heat capacity TRNSYS Transient System Simulation Program UV Ultra Violet Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 v LIST OF CONTENTS Acknowledgement ............................................................................................................. Declaration .......................................................................................................................ii Approval ...........................................................................................................................ii Nomenclature ...................................................................................................................ii Letter symbols:............................................................................................................. iii Subscripts: ................................................................................................................... iii Greek letters ................................................................................................................iv Values of Constants .....................................................................................................iv Abbreviations and acronyms; ....................................................................................... v List of figures ................................................................................................................. viii ABSTRACT .............................................................................................................. 1 1. Introduction and Background ...................................................................................... 2 1.1 Introduction: ........................................................................................................... 2 1.2 Background Information: ........................................................................................ 3 1.2.1 Fundamental parameters, concepts and terminologies used in drying: .......... 4 1.3 Solar drying: ........................................................................................................... 8 1.4 The Gulu University Orchard Solar Dryer:............................................................ 12 1.3.1 The biomass Unit: ......................................................................................... 14 1.5 Study area............................................................................................................ 16 1.5.1 Problem statement ........................................................................................ 16 1.5.2 Objective of study .......................................................................................... 16 1.5.3 Specific objectives: ........................................................................................ 17 1.5.4 Previous limitations in use of solar dryer: ...................................................... 17 1.5.6 Justification ................................................................................................... 17 1.5.7 Scope ............................................................................................................ 17 2. Literature review ........................................................................................................ 18 2.1 Previous and current models: .............................................................................. 18 2.2 Current modeling techniques used in Agro and Food-processing:....................... 21 2.2.1 Mathematical Modeling (method considered in this study); ........................... 21 2.2.2 Artificial Neural Networks (ANN); .................................................................. 21 Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 vi 2.3 Application of ANNs in Agro/Food Processing: .................................................... 22 3. Methodology: ............................................................................................................ 25 3.1 Method Summary: ................................................................................................ 25 4. THEORETICAL study of the orchard solar dryer; ...................................................... 26 4.1 Defining the Dryer System: .................................................................................. 26 4.2 Mathematical Model Formulation for the solar dryer thermal components: .......... 26 4.2.1 Fundamental System Constants, parameters and characteristics calculation: ............................................................................................................................... 26 4.2.2 Important Dimensionless heat and mass transport parameters; ................... 28 4.2.3 Heating Chamber model: .............................................................................. 29 4.2.4 Drying chamber model: ................................................................................. 31 4.2.5 Drying air properties: ..................................................................................... 33 4.2.6 Heat transfer coefficients, constants and psychometrics: ............................. 34 5. THE Computer Modeling /Simulation of the Orchard Solar Dryer: ............................ 36 5.1 Model Solution methodology: ............................................................................... 36 5.2 Transformation of physical solar system to computational domain: ..................... 37 5.2.1 Finite difference equation formulation for the entire dryer: ............................ 37 5.2.2 Pineapple Surface Area for moisture loss: .................................................... 39 5.2.3 Solar dryer performance analysis: ................................................................. 40 5.2.4 Dryer Efficiency: ............................................................................................ 41 5.3 Model Translation. ............................................................................................... 42 5.3.1 Validation; ..................................................................................................... 42 5.3.2 Model solving pseudo code algorithm: .......................................................... 44 5.3 Pineapple: ............................................................................................................ 45 5.3.1 Pineapple density and specific heat: ............................................................. 46 5.4 Dryer optimization: ............................................................................................... 46 5.4.1 Optimization script pseudo code algorithm;................................................... 47 6. Experimentation; ....................................................................................................... 48 6.1 Dryer renovation: ................................................................................................. 48 6.2 Photovoltaic fan system installation: .................................................................... 49 7. Results and Discussions ........................................................................................... 51 Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 vii 7.1 Analysis and Interpretation................................................................................... 52 7.1.1 Natural Convection; ....................................................................................... 59 7.1.2 Forced Convection; ....................................................................................... 59 7.2 Model Sensitivity Analysis; ................................................................................... 59 7.3 Computer/Computational requirements: .............................................................. 59 8. Conclusions; .............................................................................................................. 61 8.1 Concluding remarks from experimentation and computer model results comparison; ............................................................................................................... 61 8.2 Recommendations; .............................................................................................. 61 8.3 Project Cost Spreadsheet: ................................................................................... 62 APPENDIX 1: Computer model MATLAB Script / Algorithm. ..................................... 62 APPENDIX 2: Script to estimate drying air temperature, density, humidity ratio, enthalpy, RH, specific volume and shc along the dryer’s length. ............................... 69 APPENDIX 3: Making MATLAB simulations faster using parallelization and GPGPU. ................................................................................................................................... 72 APPENDIX 4: Equations for most used MSI models. ................................................ 73 APPENDIX η: Relations for calculating Nusselt’s Number; ........................................ 74 Bibliography .................................................................................................................. 75 LIST OF FIGURES Figure 1.01: Diagrammatic expression of Green House effect in solar dryers. ............... 8 Figure 1.02: Flowchart Depicting General Classification of Solar Dryers, (Habtamu Tkubet Ebuy, 2007 p. 15). ............................................................................................... 9 Figure 1.03: Classification of solar collectors, (Ashish Kumar, 2009 p. 2). .................... 10 Figure 1.04: Flow Diagram for factors considered for selection of solar dryer, (Roger Gregoire p. 17). ............................................................................................................. 10 Figure 1.05: Drying process illustrated on a psychometric chart, (N.S. Rathore, et al. p. 126). .............................................................................................................................. 11 Figure 1.06: Drying rate vs. Moisture content. ............................................................... 11 Figure 1.07: Heat and mass flow processes involved in sun drying, (Werner Weiss, et al. p. 11). ....................................................................................................................... 12 Figure 1.08: A top view of the dryer showing cross-sectional views and dryer outline. . 13 Figure 1.09: A side-view of the dryer showing basic information (View W-W)............... 13 Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 viii Figure 1.10: A front view of the dryer (View X-X), and longitudinal cross-sectional view of the biomass unit (Q-Q). ............................................................................................. 14 Figure 1.11: Transverse Cross-sectional View of the biomass Unit (View P-P) ............ 15 Figure 1.12: The biomass tray ....................................................................................... 15 Figure 2.01: Basic Neural Network Schematic .............................................................. 21 Figure 2.02: Procedure for application of numerical simulation techniques to solve engineering problems (Prof. Michael Schäfer, 2006 p. 7) ............................................. 23 Figure 2.03: Requirements and interdependencies for Numerical Simulation of practical engineering problem, (Prof. Michael Schäfer, 2006 p. 9). ............................................. 24 Figure 2.04: Relation between related disciplines and numerical simulation of engineering problems, (Prof. Michael Schäfer, 2006 p. 10) .......................................... 24 Figure 3.01:Cross-section of drying bed........................................................................ 27 Figure 3.02: Energy balance across Transverse cross-section of the drying chamber. 29 Figure 3.03: Energy balance across longitudinal cross-section of the drying chamber. 30 Figure 3.04: Energy balance across transverse section of the drying chamber. ........... 31 Figure 3.05: Computational domain of the entire dryer. ................................................ 37 Figure 3.06: Gross and Net efficiency of a typical air collector vs. Air flow rate, (Werner Weiss, et al. p. 71)......................................................................................................... 41 Figure 3.07: Flowchart for Model Solving algorithm: ..................................................... 43 Figure 3.08: Table of physical properties of pineapple .................................................. 45 Figure 3.09: Optimum conditions for solar drying of quality pineapple .......................... 45 Figure 3.10: Fresh pineapple slices loaded on a drying mesh. ..................................... 48 Figure 3.11: DC fans blowing air over drying sliced pineapple. ..................................... 49 Figure 3.12: Operating characteristics of the Fifara FD1238D12HS DC fan. ................ 50 Figure 3.13: Solar panel layout to drive fans. ................................................................ 50 Figure 3.14: Circuit Layout of solar fan system. ............................................................ 50 Figure 4.01: Spread Sheet showing hourly variation of weather on 26 th/05/2012 ......... 51 Figure 4.03: Insolation during drying: ............................................................................ 52 Figure 4.04: Wind speed and RH from 12:15 to 17:35 .................................................. 52 Figure 4.04: Experimental Moisture Content Spreadsheet of a half pineapple slice. .... 53 Figure 4.05: Simulated Moisture Content of a half pineapple slice ................................ 53 Figure 4.06; Modeled and experimental natural convection drying curve, wet basis from 12:15 to 17:35: .............................................................................................................. 54 Figure 4.07; Modeled and experimental natural convection drying curve, dry basis from 12:15 to 17:35: .............................................................................................................. 54 Figure 4.08; Modeled and experimental forced convection drying curve, wet basis from 12:15 to 17:35: .............................................................................................................. 55 Figure 4.09; Modeled and experimental forced convection drying curve, dry basis from 12:15 to 17:35: .............................................................................................................. 55 Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 ix Figure 4.11: Modeled Natural Convection drying conditions in the dryer from 12:15 to 17:35; ............................................................................................................................ 56 Figure 4.10: Modeled Instantaneous drying rate for one drying mesh of pineapple; ..... 56 Figure 4.12: Modeled pineapple temperature with time................................................. 57 Figure 4.13: Modeled Temperature distribution in an unloaded dryer under natural convection with E=750W/m2, v=0.07m/s and RH=0.61445. .......................................... 57 Figure 4.14: Modeled w, specific volume and air density in the dryer, RH=0.61445. .... 58 Figure 4.15: Modeled Air enthalpy in the empty dryer RH=0.61445, v=0.056, E=750; .. 58 Figure 4.16: Table of Summarized Gulu University Orchard Solar Dryer properties: .... 60 Table 5.01: Project Cost Spreadsheet........................................................................... 62 Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 x ABSTRACT In this paper, a mathematical model for the heating and drying of pineapple in the Gulu University Orchard tunnel solar dryer is developed. The heat and mass transfer in the dryer is used in a energy balance method to develop two systems of equations. The first is three equations in the drying chamber and the second is five equations for the drying chamber, 3 of which are differential equations. The equations are solved using a forward finite difference technique to create difference equations. The numerical solution to this equations is programmed in MATLAB to create a computer simulation of the drying and heating in the dryer. The s.h.c and density of the pineapple are continuously estimated using constituent mass fractions. The solar dryer was then renovated and then 3 DC fans run directly by a 10W monolithic PV module were installed. Pineapple was dried from 12:15 to17:35 on 26th/05/2012 using forced convection in one dryer and natural convection in another similar dryer as a control to gather experimental data. The moisture content reduced from 579.34% to 263.43% db using the fanned system while for natural convection, the moisture content reduced form 579.34% to 319.35% db. and the pineapple had begun browning. On comparison with experimental results, the simulation model had a RMSE of 0.094 db, R of 0.9966 and R2 of 0.9933. The model fitted the experimental data well and the agreement was good. It required an average of 20 to 22 seconds to execute fully on Pentium Dual Core E5700 using a time step of 60 seconds and a position step of 2mm to simulate 5.33 hours of drying one mesh of 80 pineapple slices. After a sampling sensitivity analysis, the least insensitive and most apt time step was 60 seconds and position step of 2mm, smaller values require more time and way more computer memory. Using data from the model, the dryer is more optimally used with higher airflow rates that improve heat transfer rates, greatly reduce drying time and reduce the high temperatures that brown the pineapple. The average drying air temperature using natural convection is 45-500C and 35-430C using forced convection. Forced convection had drying rates from 130 to 78 g/hr while natural convection had drying rates from 95 to 60g/hr. The model developed can be used to design solar dryers/heaters of required drying air temperatures, airflow, drying rates and can predict psychometric parameters like air density, enthalpy, RH, humidity ratio along a dryers length. Keywords/Key terms: Mathematical model, heat transfer, mass transfer, energy balance, forward finite difference, MATLAB, computer simulation, drying rate, browning, psychometric. Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 1 Chapter I: 1. INTRODUCTION AND BACKGROUND 1.1 Introduction: At harvest, most fruits and vegetables contain more moisture than is safe for prolonged storage but favorable for fungi growth, to store this fruits and vegetables they can be frozen, canned or dried. Drying can be done by freeze, sun, solar, spray or other quick industrial drying/dehydration methods. Of all the drying methods, only sun and solar drying utilize the free earthly insolation and thus do not require electrical energy. Natural sun drying of agricultural produce is the most widely used preservation technique used worldwide since it involves the least costs and the energy is free. It is more acceptable for prolonged storage than any other preservation methods. Freezing is commonly viewed as the most convenient preservation method, but freezers require a constant source of electricity and frozen food still has a shorter shelf life than dried food since the psychrophilic bacteria are temporarily inactive. Solar drying uses solar energy that is incident and trapped due to the greenhouse effect to dehydrate material in a dryer to required moisture levels. Thus it can be a natural phenomenon or artificially manipulated. Sun drying is open drying of moist material that is exposed to the sun’s rays; the material can be on mats, tarpaulins or the ground. Simulation in regard to computing is the technique of representing the real world by a computer program or the process of designing a model of a real system and conducting experiments with this model for the purpose of understanding the behavior of the system and evaluating various strategies for the operation of the system. “Mathematical modeling and computer simulation of agricultural products drying is now widely used in agricultural engineering research. The development of a simulation model is a powerful tool for predicting performance and can help designers to optimize the dryer geometry at various operating conditions without having to test experimentally the dryer performance at each condition. Simulation enables the researcher to evaluate the performance of the solar dryer before actual production of the prototype and the experiment is done. If simulation is combined with optimization, the researcher is able to design a cost effective solar dryer, that is, a solar dryer with minimum cost and maximum moisture removal within given constraints”, (M A Hossain, et al., 2009). The purpose of this project is to create a model of the solar dryer first; then verify it after drying pineapples in the renovated and improved dryer, then determine the optimal air velocity and thickness of pineapple for shorter drying time and higher efficiency from simulated experiments. Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 2 The tunnel solar dryer was originally designed in 1993 by Mühlbauer W, Esper, A. and J. Müller, at the institute of Agricultural Engineering in the Tropics and Subtropics, University of Hohenheim, Germany who were trying to improve the low buoyancy of ordinary natural convection based dryers. Their design included a photovoltaic based solar fan system that required 40W at 12V to aid the air flow required to remove evaporated water, (B.K. Bala and S.Janjai p. 62). The drier has been tested and attained economic viability and is used in Asian and African countries. However a low cost version of the drier has been designed at Bangladesh Agricultural University, Mymensingh. The drier has a flat plate collector, a tunnel drying unit and a small fan to provide the required air flow over the product, (B. K. Bala, et al., 2009). Advantages of simulation over field experimentation:  Allows test of new and existing designs and layouts without using physical resources, thus more economically and technically viable.   Allows identification of bottlenecks in processing.  Allows us to control time by slowing down or accelerating phenomena for study.  Tests hypothesis about how, why, where , what if and many other questions Gives us insight into how physical systems works better Shortcomings of modeling and simulation:  Simulation modeling is an art required specialized training    Gathering highly reliable input data is time consuming and intensive, sometimes even not feasible or impossible. The models are input-output models, thus they run rather than solve making it an analysis tool not a decision maker as commonly perceived. Simulation requires a lot of computational resources for reliable results and produces and requires lot of data. 1.2 Background Information: Drying is the oldest preservation technique of agricultural products and it is energy intensive. High prices and shortages of fossil fuels have increased the emphasis on using alternative renewable energy resources. Drying of agricultural products using renewable energy such as solar energy is environmental friendly and has less environmental impact. (B. K. Bala, et al., 2009 p. 1) Drying of agricultural products is still the most widespread and affordable preservation technique and it is becoming more and more attractive alternative to marketing fresh Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 3 fruits, vegetables and fish since the demand of high quality dried fruits, vegetables and fish is permanently increasing all over the world, (B.K. Bala and S.Janjai). The following are highlights of solar and sun drying and modeling;  Sun drying is the most widely used natural method of food preservation in the world, but is widely used at a rudimentary and basic level on the ground, mats or roofs.  The quality and efficiency of the drying process remains lacking.  Natural convection solar dryers and a recent innovation and enhancement, the solar tunnel drier currently used in the Gulu University Orchard with a v-grooved (iron-sheet) absorber or drying bed are widely used but for most of them, in depth performance parameters are not determined and availed to the users.  Computer modeling is part of simulation and involves representing a proposed system, phenomenon or an existing system’s operation and behavior in a programming language mathematically or algorithmically using computing tools, here it is used to develop a simulation model to give a deeper insight in to drying.  Simulation is the process of implementing/executing the model as a computer program, and conducting experiments with the model for the purpose of understanding the behavior of the system, or evaluating strategies for the operation of the system. 1.2.1 Fundamental parameters, concepts and terminologies used in drying: Some very important terms frequently used in crop drying calculations and their relationships are described below. Most of these terms can be represented on a psychometric chart. Vapor Pressure (Pv): The vapor pressure is the partial pressure exerted by the water vapor molecules in moist air. When air is fully saturated with water vapor, its vapor pressure is called the saturated vapor pressure Pvs. The natural tendency for pressures to equalize will cause moisture to migrate from an area of high vapor pressure to an area of low vapor pressure. Relative Humidity (RH): Relative humidity is defined as the ratio of the mole fractions of water vapor in air to the saturated air at the same temperature and pressure or the ratio of Pv of water vapor in air to that of water vapor in saturated air. Humidity Ratio (w): Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 4 This is the mass of water vapor contained in moist air per unit mass of dry air. (Kg H2O/ Kg Dry air) Dew-Point Temperature (Tdp): The dew-point temperature is the temperature at which water vapor, being cooled at a constant mixture pressure and humidity ratio, begins to condense at constant w and atmospheric pressure. Dry Bulb Temperature (Tdb): Dry bulb temperature is the temperature of a gaseous mixture, fluid or substance measured by an ordinary thermometer. Wet-Bulb Temperature (Twb): The psychometric wet -bulb temperature is the temperature of moist air indicated by a thermometer whose bulb is covered by a wet wick. The thermodynamic wet bulb temp T*wb is the temperature reached by moist air and water when the air is adiabatically saturated by evaporating air. Wet-Bulb Depression: The wet-bulb depression is the difference between the dry-bulb and wet-bulb temperatures. Enthalpy (H): The enthalpy is the heat content of the moist air per unit mass of dry air above a certain datum temperature. The enthalpy of moist air per unit mass is the sum of the enthalpies per unit mass of dry air and super-heated water vapor. It is the sum of internal energy and the product of volume and pressure. Specific Heat Capacity: The specific heat capacity, C, is the quantity of heat needed to increase the temperature of a unit mass of a material by one degree. Sensible Heat ( Qs): The sensible heat is the heat energy absorbed or released when a body changes temperature without any change in physical state. Latent Heat of Vaporization (Lp): The latent heat of vaporization is the quantity of heat required to change a substance from a liquid to a vapor at constant temperature. Moisture Content (m): Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 5 The moisture content is a measure of the water content of a material. It can be calculated on either a wet or dry basis. The wet basis moisture is the ratio of mass of water to wet mass of the entire sample. The dry basis is the ratio of the mass of water to dry matter mass in the entire sample. Equilibrium Moisture Content (me): The equilibrium moisture content (EMC) is the moisture content of a material/product after it has been exposed to a given environment with consistent temperature and relative humidity for an infinitely long period of time. me can also be the MC at which the internal product vapor pressure is in equilibrium with it’s environment’s vapor pressure. Drying Rate (DR): This is the rate of change of moisture content of a drying material or rate of loss of moisture from a moist material. It can be expressed per unit time of Kg H20/unit time. Mass Shrinkage Ratio (SR): This is the ratio of mass of drying material after a given time to the initial mass of the material. Equilibrium Temperature of Drying Air The drying process takes place at a temperature that is between the temperature of the air entering the crop bed and that of the air exiting the dryer. The equilibrium temperature of drying air can be calculated by establishing a heat balance between the initial conditions and the equilibrium conditions and assuming that the temperature of the equilibrium equals that of the grains and the humidity ratio at equilibrium equals that of drying air. Drying Constant (k): The drying constant is a property of mass diffusing and geometrical properties of the product and it depends on the drying air conditions especially temperature. It can be determined using the Newton-Raphson method, graphical method (using experimental data) or using established empirical relations for given crops. The general drying equation (Newton) is; – – , thus The equation above has been modified to suit varying crops and conditions by various researchers and scholars. Equilibrium Relative Humidity (ERH): Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 6 Equilibrium relative humidity is that humidity value for which air is in equilibrium with a sample. The equilibrium relative humidity occurs when the sample neither gains nor loses moisture, thus the sample has equilibrium moisture m e. Water Activity (Aw): Water activity is simply a measure of the energy status of the water in a system. It is defined as the vapor pressure exerted by the food to the saturated vapor pressure of water at the same temperature. As the temperature of a moist substance increases, aw typically increases except in some products with crystalline salt or sugar. Aw is the percentage value of ERH. Aw Thin layer drying: This is the drying of a uniformly thick layer of material exposed fully to an airstream during drying. The depth (thickness) of the layer should not exceed three layers of material, (ANSI/ASAE S448, 2001(R2006)). If drying material is more stacked than this, it becomes deep bed drying. Moisture Sorption Isotherm (MSI): This is a plot/curve of moisture content of a material against the relative humidity or water activity at constant temperature. The equation of this curve becomes the MSI model for the drying material used to predict instantaneous me of the drying product. Many sorption isotherm models have been formulated but the most accurate are the GAB (Guggenheim-Anderson-deBoer), modified Chung-Pfost, modified Oswin, modified Henderson and modified Halsey, they are recommended by ASABE. Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 7 1.3 Solar drying: This is drying of moist material in a solar dryer in contrast to open sun drying. Radiant energy from the sun passes through the cover surface but infrared re-radiation from the absorber surfaces and drying bed cannot, causing a greenhouse effect. This trapped heat and incident insolation cause incoming air temp to rise, the hot air while flowing over products causes sensible heating and subsequently drying. Figure 1.01: Diagrammatic expression of Green House effect in solar dryers. Drying involves simultaneous heat and mass transfer. Mass transfer is moisture loss while product temperature increases with time. Moisture is lost to flowing air through evaporation. The air flow is caused by convection due to buoyancy of air induced by the change in density of air inside the dryer making it lighter due to increased temperatures in the dryer, causing a thermo-siphon effect. Heated air expands and become less dense, and thus more buoyant than the cooler air coming in through the dryer’s entrance. Convection moves heated air upwards towards the drying chamber as it is simultaneously replaced by incoming air. A Chimney increases buoyancy effect, due to the stack effect and lets out hot humid air out of the dryer crating a continuous mass flow as room is created for incoming air. Heat flows through convection, radiation and conduction for the different active and insulation parts of a solar dryer. Radiation is the transfer of heat by electromagnetic waves. The range of wavelength 0.8–400 mm is known as thermal radiation, since this infrared radiation is most readily absorbed and converted to heat energy, (Dr. Jorge E. Lozano, 2006 pp. 73-74). Emissivity values of foods are in the range 0.5–0.97, (Dr. Jorge E. Lozano, 2006 pp. 7374).Solar drying preserves food with readily available energy from the sun. Storing of foods with high moisture content can lead to molds, discoloration, mustiness and malodor, toxicity, spoilage and nutrient loss of the food, (Roger Gregoire). Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 8 There is a growing and urgent need of a simple inexpensive process to save this spoilage and drying is such a process. (B.K. Bala and S.Janjai) Drying of agricultural products is still the most wide spread preservation technique and it is becoming more and more attractive alternative to marketing fresh fruits and fish since the demand of high quality dried fruits and fish is permanently increasing all over the world, (B.K. Bala and S.Janjai). As the air is passed over the product rather than through the product in the drier, the power requirement to drive a fan is low, (B. K. Bala, et al., 2009 p. 4). Despite their low energy requirements, solar dryers continue to struggle to gain acceptance by commercial producers of dried products. The reasons for this are complex and varied, and depend on many factors (Battock, 1990; Bena & Fuller, 2001). Figure 1.02: Flowchart Depicting General Classification of Solar Dryers, (Habtamu Tkubet Ebuy, 2007 p. 15). Moisture in foods occurs in three types; physically bound (bulk water), chemically bound and capillary trapped water. Bulk water is the water readily available as moisture and the gets easily evaporated during drying. Successful drying depends on enough heat to draw out moisture without cooking the food, dry air to absorb water and adequate air circulation to carry of moisture. A solar dryer basically consists of glazing, an absorber bed, a chimney, insulation and protective material (wood is normally used). A fan system is optional depending on the considerations made during the design, performance and operation of the dryer. The type and orientation of the glazing is the most crucial material related factor in determining the performance and thermal capacity of the dryer. Currently the best glazing is polycarbonate sheets; they have a transmittance of 0.92-0.96 and are very durable Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 9 and weather resistant. Glass is also a very good glazing material and it is strong and durable though brittle. The most economic option is polythene which has a high transmittance and is relatively durable. The arrangement and orientation of the glazing determines it performance and applicability. Figure 1.03: Classification of solar collectors, (Ashish Kumar, 2009 p. 2). Many types of solar dryers exist but for a given scenario, one needs a specific dryer for optimum performance. Figure 1.04: Flow Diagram for factors considered for selection of solar dryer, (Roger Gregoire p. 17). Solar drying of agricultural products involves dehydration through use of air. The properties of air change as it gains moisture from the food; a psychometric chart represents all this changes from the start to the completion of drying. Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 10 Figure 1.05: Drying process illustrated on a psychometric chart, (N.S. Rathore, et al. p. 126). Drying occurs in three stages, initial stage, constant drying rate and finally falling rate drying stage. First phase exterior water is evaporated. Then moisture starts diffusing outwards towards the surface, overheating at this stage causes case hardening. Figure 1.06: Drying rate vs. Moisture content. Many factors like temperature, air flow rate, nature of the food affect the drying rate. Another important parameter considered during drying is diffusivity which is used to indicate the flow of moisture out of the material being dried. In the falling rate period of Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 11 drying, moisture is transferred mainly by molecular diffusion. Moisture diffusivity is influenced mainly by moisture content and temperature of the material. Drying involves simultaneous heat and mass transfer as show below. Figure 1.07: Heat and mass flow processes involved in sun drying, (Werner Weiss, et al. p. 11). Heat flow processes Mass flow processes Solar drying protects the food from rain fog or dew unlike sun drying. Heat flow processes are similar to solar drying except, for less radiation loss from the product, greenhouse effect causing infra-red heating, less heat loss from product due to wind contact and higher air flow. 1.4 The Gulu University Orchard Solar Dryer: The dryer is an improved hybrid solar tunnel type with a biomass energy backup unit. It spans 9m, is 1.2m wide and 58cm off the ground level form the lowest end. It uses a flat plate solar collector made of UV stabilized polythene, a corrugated galvanized iron drying bed, wooden sides with the interior painted black to act as absorbers. A corrugated bed has a higher heat transfer coefficient than a flat drying bed type dryer (Werner Weiss, et al.), this due to increased surface area It has a bare plate single glazed transparent cover. The UV stabilized polythene is placed at an angle of 4.5 0 to make a slanting roof to ease rain drainage. The drying bed is insulated with one strand of papyrus after the biomass unit. The angle of inclination is 2.80 and the orientation towards the sun. The products in the drying chamber are dried by combination of heated air form the heating chamber, incident radiation from the sun that goes through the cover, radiation form the black sides and re-radiation from the drying bed. Air enters the heating chamber by natural convection due to buoyancy caused by air in the dryer heating up, thus becoming less dense. Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 12 The drawing below shows the side view of the dryer: Figure 1.08: A top view of the dryer showing cross-sectional views and dryer outline. All dimensions in this drawing and later ones are in millimeters (mm) and use an approximate scale of 1:60 The drying above shows the dryer as seen from above it is 9.3m long, 118cm wide with wooden sides that are 2mm thick, has 3 Polyvinyl Chloride (PVC) chimneys at end to release moisture laden air. Figure 1.09: A side-view of the dryer showing basic information (View W-W) The dryer has a heating chamber about 285cm long where incoming ambient air is heated, then to the biomass air gap meant to allow heat flowing by radiation from combustion of biomass to dry the products then finally the drying chamber of about 6m where products are loaded for drying. The dryer has sides painted black in the interior to act as absorbers, a corrugated (vgrooved) galvanized drying bed insulated by a thin layer of papyrus reeds placed under the bed only in the drying chamber. The windows in the dryer are used for loading and offloading and are normally left open during the drying depending on the product being dried. Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 13 Figure 1.10: A front view of the dryer (View X-X), and longitudinal cross-sectional view of the biomass unit (Q-Q). X-X Q-Q This shows the entry of air where dust is filtered out first, where the air is heated, fed to the drying chamber to heat bio-materials then absorb moisture up to the chimneys 9m ahead and 92cm above the air entry point. The silver part is the biomass unit concrete wall connected to an iron chimney. 1.3.1 The biomass Unit: A biomass burner is placed 2.9m from the air entry point, just after the heating chamber and is insulated with bricks and mortar. It is made of a horizontal iron cylinder 8mm thick, 56cm diameter, 82cm long with a biomass tray located 25cm above the base and finally a chimney 46cm above the base as the drawings above show. The chimneys are not considered in this drawing. On cloudy days, rain season, after dawn or on very windy days, biomass energy can supplement or entirely run the dryer. To use the biomass unit, the door is opened the biomass (firewood, charcoal, combustible bio-waste like saw-dust, coffee husks or any other plant derived combustible) is feed on to the biomass tray and ignited. The biomass is placed on the tray above; it therefore requires large particles to be retained on the tray. Al least 3cm wide making firewood suitable as the base then adding other bio-particles on top of it. The biomass heating chamber is placed between the collector and the drying unit. Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 14 Figure 1.11: Transverse Cross-sectional View of the biomass Unit (View P-P) Figure 1.12: The biomass tray Depending on the biomass being used, the door can be left open or closed since an air flow gap exists for air intake to facilitate the combustion process. Biomass energy is less often used mainly because the incident radiations on average is high and students normally find it cumbersome to use it, even on days when it is more than appropriate. The biomass unit is an 8mm thick iron cylinder with two openings, the air entrance and the chimney making it impossible for smoke to reach the drying products thus preserving the organoleptic properties of the drying food. Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 15 The main focus of the model to be formulated is mainly solar radiation as the energy source. The bio-mass energy modeling option will thus not be looked with a bias on solar energy since it is the most convenient, cleaner, sufficient and even more frequently used. Dryer Capacity and drying rate: The dryer capacity for pineapple will be established during the experimentation. The capacity will be expressed as load per drying session (kg) and other appropriate drying capacity representations. Drying: Products to be dried are placed on drying mesh (plastic mesh nailed to wooden frames). The products are placed in a single layer in each plastic mesh. For small fruits or vegetables it may be feasible and more effective to use layered drying to increase efficiency and throughput. The drying mesh on average measures 90cm by 114cm; the wooden sides are 5cm thick and 2.5cm off the ground. This gives a total area of 80cm by 104cm (0.832m 2) available for drying for each mesh. Currently Dried products: Pineapples, jackfruit seeds, bananas. Other dried products to consider: Vegetables like mushroom (edible fungi) that very nutritious and okra. Fruits like mango (sliced mango), jackfruit, bananas, vegetables, oil seeds, spices (chili, ginger, cauliflower) can be dried easily since they are all vegetables, fruits and herbs. The solar tunnel dryer is made using simple tools and locally available materials. 1.5 Study area 1.5.1 Problem statement The Solar drier in the Gulu University orchard dries pineapples, bananas, several other fruits and vegetables but no documentation and data exists on its performance, working conditions and optimum performance parameters. The drier uses natural convention which requires longer drying times as opposed to forced convention or mixed mode drying. The performance of the dryer cannot be readily predicted 1.5.2 Objective of study Objectives of the study and experimentation include;  Develop and verify a computer model of the current solar dryer in the orchard. Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 16   Renovate and improve the dryer. Determine the optimum airflow rate (velocity of air) and thickness/size of drying product on the performance of the transient system. 1.5.3 Specific objectives:     Re-paint and improve insulation of the dryer’s absorber (iron sheet bed). Install photovoltaic based DC fans to improve air flow and reduce the drying time and product browning in the dryer especially when radiation is high. Collect moisture content and product temperatures from drying experimentation, and then use that data to validate the model. Be able to predict performance of solar dryer based on prevailing conditions and the food being dried. 1.5.4 Previous limitations in use of solar dryer: 1. No measured performance and psychometric data existed. 2. The dryer required renovation. 3. Natural convection does not provide sufficient airflow due to limited buoyancy. This can be overcome by additional convection using fans to aid airflow. 1.5.6 Justification 1. Software simulation is more efficient, fast and economical to predict drying results and performance than physical experimentation. 2. Parameters not easy to vary physically like insolation, wind speed can be easily manipulated in a computer model. 3. Computer models encompass more possibilities than actual experimentation can. 1.5.7 Scope  The study is limited to formulation of a mathematical model, and using it in MATLAB to generate simulated data, then validating it.  Using the validated model, the optimum air velocity and thickness of pineapple during drying can be determined.  The biomass based drying process will not be modeled; the model will concentrate on incident solar radiation mainly. Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 17 CHAPTER II 2. LITERATURE REVIEW 2.1 Previous and current models: Many mathematical, empirical and some neural networks have been used to model agricultural dehydration, mass and heat transfer processes and systems. For solar drying, mathematical models have been used since the 1980’s by scholars like B.K. Bala and neural networks since the 1990’s to simulate solar dryers. The drying kinetics of food is a complex phenomenon and requires time dependent representations to predict the drying behavior and for optimizing the drying parameters. The prediction of drying rate of agricultural materials under various conditions is important for the design of drying systems, (Ronoh EK, et al., 2010). Currently simulation of physical, industrial and many other types of processes and systems is widely used to predict, emulate, design and visualize the actual processing, performance, failure and other required criterions. Solar drying modeling has been and is successfully being practiced using mathematical models, artificial neural networks or a hybrid method utilizing both the neuro and mathematical technique. Some previous models are reviewed below. S. Sadodin and Kashan T. T developed a numerical model to study the drying of Copra in a solar greenhouse tunnel drier. In Sadodin’s model, a system of partial differential equations describing heat and moisture transfer during drying copra in the solar greenhouse dryer was developed and this system of nonlinear partial differential equations was solved numerically using the finite difference method. The numerical solution was programmed in Compaq Visual FORTRAN version 6.5. The simulated results reasonably agreed with the experimental data for solar drying copra. Sadodin’s model could be used to provide the design data and is also essential for optimal design of the dryer, (S. Sadodin, et al., 2011). Md Azharul Karim and M.N.A Hawlader developed a mathematical model taking into account shrinkage of material and shrinkage dependent effective diffusivity to solve the heat and mass transfer equations for convective drying of tropical fruits. The model had two components, equipment model to predict instantaneous temperature and humidity ratio of air at any location of the tunnel and the material model capable of predicting the instantaneous temperature and moisture distribution inside the material. The predicted results were compared with experimental data for the drying of banana slices dried in a solar dryer. Experimental results validated the model they developed, (Md Azharul Karim, et al., 2005). Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 18 M. A. Hossain, K. Gottschalk and B. M. A. Amer developed a mathematical model for a concentrative flat plate solar collector coupled with an indirect multi-rack type hybrid dryer drying tomato. Two sets of partial differential equations for the collector and dryer were developed to predict cover, receiver, air and tomato temperature, moisture content and RH values. The first set of equations were solved iteratively and the second set of equations were solved numerically based on an exponential solution over the finite difference grid element using the outlet air conditions of the collector as inlet air conditions of the dryer. The simulated cover, air, relative humidity, and product moisture content and receiver temperatures agreed well with the measured temperature. This model can be used to provide design data of the solar and hybrid dryer for the drying of tomatoes as well as other fruits and vegetables, (M A Hossain, et al., 2009) Habtamu Tkubet Ebuy developed a model to simulate a solar cereal dyer using TRNSYS, (Transient System Simulation program). The simulated solar dyer consisted of the solar air heater which used low emissivity glass cover, weather data, and an integrated dryer chamber attached to the collector where the products to be dried are placed. He wrote a computer program using C++ to predict the collector outlet temperature, mass flow rate and other engineering variables from the input of the meteorological data and collector parameters and also done for the dryer chamber by using the input from the collector output and the properties like initial moisture content, initial temperature of cereals and other engineering properties. He presented the system simulation results in graphical form suitable for system performance analysis. (Habtamu Tkubet Ebuy, 2007) TRNSYS is an extensible simulation environment based program for the transient simulation of systems, including multi-zone buildings. It is used by engineers and researchers around the world to validate new energy concepts, from simple domestic hot water systems to the design and simulation of buildings and their equipment. B. K. Bala, Serm Janjai, Ashraf M.A and M. A Uddin in their 2005 article presented a multilayered neural network approach used to predict the performance of the solar tunnel drier for drying jackfruit bulbs and leather. The drier had a loading capacity of 120–150 kg of fruits and used two DC fans operated by a PV module. Sixteen experimental runs were conducted for drying jackfruit bulbs and leather (eight runs for jackfruit and eight for jackfruit leather). The architecture and neuron layer details were presented. Using solar drying data of jackfruit bulbs and leather, their network model was trained using the back propagation algorithm. The prediction of the performance of the drier was found to be excellent after it was adequately trained. It can be used to predict the potential of the drier for different locations, and can also be used in a predictive optimal control algorithm, (B. K. Bala, et al., 2005). Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 19 B. K. Bala and Serm Janjai in their International Solar Food Processing Conference 2009 paper presented developments and potentials of solar drying technologies for drying of fruits, vegetables, spices, medicinal plants and fish. They analyzed current and previous efforts on solar drying of fruits, vegetables, spices, medicinal plants and fish terms of drying performance and product quality, and economics in the rural areas of the tropics and subtropics. They analyzed experimental performances of different types of solar dryers such as solar tunnel dryer, improved version of solar tunnel dryer, roof-integrated solar dryer and greenhouse type solar dryers. They presented a mathematical model used to simulate performances of the three types of dryers. The agreement between the simulated and experimental results was very good. The simulation models developed can be used to provide design data and also for optimal design of the dryer components, (B. K. Bala, et al., 2009). I.N Simate in 2003 wrote a paper presenting a comparison between optimized mixed mode and indirect mode maize solar dryers. The simulation models were validated against results from a laboratory solar simulator at the University of Newcastle UK, (I.N.Simate, 2003). Rosarin Smitabhindu in 2008 developed a mathematical model for optimal design of a solar assisted drying system. The model had 2 components, a simulation and economic model. The economic model is beyond the scope of this study. The simulation model consisted of two systems of differential equations. One was for the collector and the other for the drying cabinet. These equations were solved using the finite difference methods and a computer program in FORTRAN was developed to simulate the model. The model validation was good; the agreement between the simulated and experimental results was good. (Rosarin Smitabhindu, 2008). Allen Dong in 2009 described a scaled down versoin of the original solar tunnel designed at University of Hohenheim, Stuttgart, Germany and demonstrated how to apply the Penman-Monteith evapotranspiration equation to solar drying. The result is a relative evaporation potential of the food in the dryer that can be used for comparison but no the actual evaporation potential of the food since the dryer’s condition do not meet the requirements for open air evaporation, (Allen Dong, 2009e). Many models for solar dryers and drying have been formulated and a lot of research especially in Asia has been conducted on solar drying modeling and simulation. Most of the models are thin layer drying models describing drying but reliable simulation models to aid the design of tunnel dryers for fruits are few, (Md Azharul Karim, et al., 2005). Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 20 2.2 Current modeling techniques used in Agro and Foodprocessing: 2.2.1 Mathematical Modeling (method considered in this study); Mathematical models are set or system of equations describing the behavior/dynamics of a process, system, event and anything that can be described mathematically. The principles of operation of a machine, system or process are described using equations. The solution to these equations describes the systems behavior with respect to time, distance, resources or any other useful parameters. An algorithm calculating the solution to these equations becomes a computer model or computer program. 2.2.2 Artificial Neural Networks (ANN); These are mathematical/computational models structured to function like biological neural networks. (Interconnected neurons for signal processing) Figure 2.01: Basic Neural Network Schematic Hidden Layer/s: (Performance parameters, empirical relations e.tc) Input Layer: P (Initial conditions and variables etc.) A Output layer: (required values) X Q B R C S Y Z T The links between neurons are given weights depending on the strength of their relationship or their dependency on each other. The weights keep varying based on an algorithm chosen suitably for the network. Represents an artificial neuron. Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 21 Artificial neurons are mathematical functions conceived as crude models, or abstraction (representations) of biological neurons. An artificial neural network is an interconnected group of nodes and neurons operating in parallel, similar to the vast network of neurons in the human brain as below at input, hidden and output levels. They are usually used to model complex relationships between inputs and outputs or to find patterns in data. A neural network consists of an interconnected group of artificial neurons, and it processes information using a connectionist approach to computation. ANNs have the ability to learn from examples (data) through iteration without requiring a prior knowledge of the relationship of the parameters. Therefore they are used to generalize and establish relationship between input and output data. An ANN’s computational structure is characterized by network topology/architecture, network type, node characteristics, number and type of neurons and learning rules. 2.3 Application of ANNs in Agro/Food Processing: Due to their ability to learn and outperform mathematical models if well designed and trained, they are used in the following ways, (Joseph Irudayaraj, 2002 pp. 57-60): 1. Product grading and classification. 2. Food quality assessment. 3. Complex process models like industrial dryer performance prediction, deep bed drying of cooked rice, thermo processing of canned foods, non-Newtonian flow of liquid foods in tubes, snack food drying processes, psychometric parameter estimation, prediction of loaf volume of breads from different wheat cultivars and other sophisticated industrial food processes. 4. Process control applications. Examples of application of NNs to food processes, (Irudayaraj, 2002 pp. 61-68); Feed forward NNs based on back-propagation learning algorithm developed using NueroShell2 (Ward Systems Group, Inc., Frederick MD) were applied as below: 1) Grading of Tomatoes based on RGB Color composition; A three layer, 3-6-1 NN was used to grade 95 tomatoes at different ripening stages based on their RGB index values got by digital imaging using a machine vision system. Only 6 tomatoes were misclassified by the NN compared to 17 misclassified tomatoes from statistical estimation using statistical regression analysis. 2) Moisture content changes in deep bed drying of rough rice; A four layer, 6-16-16-2 NN trained with 1115 input datasets was used to predict the moisture content the drying rice in comparison to the results from Drying Simulation Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 22 Software package for deep bed drying of grains, developed at the Asian Institute of Technology. The NN was able to map the complex relationships in the deep bed drying of rough rice to a satisfactory level. 3) Estimation of sensory stickiness scores of cooked rice. A three layer, 4-10-3 NN trained with 70 datasets was used to predict sensory hardness, stickiness and acceptability of cooked rice. The NN’s results had a RMSE of 6.02% while statistical analysis using regression analysis had a bigger RMSE of 13.7%. NNs are however unable to extrapolate out of the data used to build the model (Irudayaraj, 2002 p. 57), this is a big limitation compared to mathematical models. NNs will not be considered in this study. To solve engineering problems using computer models, many considerations and systematic steps are involved as shown below. Figure 2.02: Procedure for application of numerical simulation techniques to solve engineering problems (Prof. Michael Schäfer, 2006 p. 7) There are many programming languages that can be used to program mathematical models used in a simulation, main stream ones include C++, FORTRAN (first high level programming language), MATLAB. These languages are not streamlined in their purpose, however for simulation several, software has been developed. This software packages provide a modeling environment that is easier to use and customize. A wide variety of simulation software currently exists in the market; some are highly specialized while a good number is mainstream and highly configurable. Dependencies and prerequisites for engineering problem simulation are show on the next page. Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 23 Figure 2.03: Requirements and interdependencies for Numerical Simulation of practical engineering problem, (Prof. Michael Schäfer, 2006 p. 9). Figure 2.04: Relation between related disciplines and numerical simulation of engineering problems, (Prof. Michael Schäfer, 2006 p. 10) MATLAB is a 4th generation programming language. It is preferred because it is the standard or de facto for industry and academia, it has inbuilt support for vast (almost all) mathematical functions, matrix manipulations, excellent graphing capabilities and the neural network toolbox useful for creating neural networks with neural network fitting, pattern recognition, training and many other useful tools. It’s complier also supports language transitioning making it possible to convert MATLAB code to C++ or C code. Thus for this study, the computer model is written in MATLAB. Little or no research on solar drying modeling and performance analysis in Uganda, particularly in Gulu has been carried out. That is the main focus of this study since solar energy is abundant, environmentally friendly and easy to harness and computer models can help predict performance to satisfactory levels. "The development of a simulation model is a valuable tool for predicting the performance of solar drying systems”, (S. Sadodin, et al., 2011). “Simulation of solar drying is essential to optimize the dimensions of solar drying systems and optimization techniques can be then used for optimal design of solar drying systems”, (B. K. Bala, et al., 2005). It is likely by the year 2100, due to dwindling availability, worldwide use and polluting effects, fossil fuel energy will be overtaken by solar energy to emerge as the most important energy source for mankind. (S.C. Bhattacharya, et al.) Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 24 CHAPTER III 3. METHODOLOGY: 3.1 Method Summary: A sequential outline of all activities involved is given below; 1. The dryer is thermodynamically analyzed; then equations for the cover, iron sheet bed, drying air, and pineapple mass and energy balance will be developed. These systems of equations constitute the solar dryer’s mathematical model. 2. A finite difference solution to the equations is developed to determine MC of the pineapple, temperature of the pineapple, cover, iron sheet bed and air and finally the relative humidity of the air along the entire dryer at any time of the drying process. 3. Develop algorithm to solve the finite difference solution for the dryer considering boundary conditions, valid assumptions, errors, time of simulation. This is a numerical solution; Iterate variables till the error is small, use this value to calculate other variables, do this for each Δx (grid spacing) along the heating chamber, take final values as initial values in the drying chamber, then for each Δx along the dryer, compute, MC, temperatures and RH. Then repeat the entire process for each Δt (time step) for the duration T (simulation time). End loops depending on time, final moisture content or temperature. All calculated values need to be stored in a matrix since they become initial values for the next loop, or will be required later on in a graph or for any reason. The calculated values can now be displayed on graphs or exported to excel for analysis. 4. Program the algorithm in MATLAB; the MATLAB scripts can even be compiled to an executable program for demonstrative use. 5. Renovate the dryer, this includes re-painting the interior sides black and the exterior grey, install the DC fans and build a stand for the solar panel. They were installed just before the drying chamber (above the biomass chamber). 6. Experiment on the drying of pineapple slices with fans on and without fans (control experiment) running and collect the moisture content and temperature of the pineapple as it is drying up to the evening of that day. 7. Run simulations under conditions analogous to ones pineapples were dried under and export the data. 8. Analyze data from the data form the pineapple experimentation and the simulation to determine RMSE, and draw conclusions on the model. Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 25 9. Use the script to simulate experiments in order to determine the most efficient/optimal velocity and thickness of pineapple. Conclude and project is done. 4. Theoretical study of the orchard solar dryer; 4.1 Defining the Dryer System: Determining the boundaries and restrictions to be used in defining the system (or process) and investigating how the system works. The system is a solar tunnel drier with a biomass unit, it is a closed system interacting thermally with its immediate surroundings (ambient air, the atmosphere and sky), and incident solar radiation and air flows in through the inlet to the heating chamber then out from the chimney. The system is a transient system that cannot be solved analytically. System components contributing to significant thermal changes and energy retaining: 1) The UV stabilized plastic cover tilted at 4.80 to edge of the drier. 2) The corrugated iron sheet bed 3) The working fluid (air flowing in, then out of the drier) 4) The single layer dry papyrus insulation under the iron sheet bed 5) The material being dried(fruit, vegetable, etc.) depending on it’s physical shape, thermodynamic properties and it’s moisture content m. The bottom papyrus-mat insulation resist’s heat loss by convection between the galvanized bed and the surroundings below it, the wooden sides are good insulators and minimize heat loss by convection to surroundings. Each of the active components will have a mathematical model describing it’s heat and mass transfer/transport. A collective model will then be formulated to describe the temperature, mc and RH along the drying tunnel during the drying process for given times. The energy balance method is based on subdividing the medium into a sufficient number of volume elements and then applying an energy balance on each element The model will be based on energy, mass balance and heat transfer (for the working fluid (air) appropriately applied to each of the active thermal components. 4.2 Mathematical Model Formulation for the solar dryer thermal components: 4.2.1 Fundamental System Constants, parameters and characteristics calculation: Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 26 1. Cross sectional area of corrugated bed (AB); Considering the drawing on the next page; Figure 3.01:Cross-section of drying bed 2 AB= 2 = Width of corrugated bed (Lc): WC=( √ Surface Area of bed: ) 2 ABH WC LH 2 ABD WC * LD 2 Area of biomass insulation cover = ABB = 2. Average Cross-sectional area of heating chamber (AHC): The average height between the cover and iron bed is 2 AH= 3. Average Cross-sectional area of drying chamber (ADC): The average height between the cover and drying is 2 ADC= 4. Hydraulic Diameter; Heating Chamber HD: HH= Drying Chamber HD: HD= 5. Collector area ( ) ( ( ) ( ) ) Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 27 Heating chamber: 2 ACH= Drying chamber: 2 ACD= AC= ACD 2 ACH= 6. Volume: Heating chamber VH= AH*LH= 3 Drying chamber VD=AD*LD= VT= VH+ VD= 3 3 7. Vent Area; 4.2.2 Important Dimensionless heat and mass transport parameters; Used in determining convective heat transfer coefficients. Used to characterize flow (laminar or turbulent), useful in forced convection. Used in natural convection fluid flow. Used in fluid heat flow calculations and characterization. Useful in buoyancy induced fluid flow like that of natural convection dryers. Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 28 Moisture content (MC) values used will be on wet basis (wb.) and dry basis (db.), depending on the required measure, wb is used in calculating pineapple s.h.c and density and db is used in drying equations. The mathematical model is in two sequential parts; the heating chamber and the drying chamber respectively. 4.2.3 Heating Chamber model: Assumptions made: 1. Chemical properties of moisture and air are constant. 2. Air flow is one dimensional, only along the axis of the dryers’ length. 3. The problem is one dimensional and conduction heat transfer within the bed is negligible. 4. The black walls absorb and re-radiate all the energy incident on them and the fraction of solar radiation lost through the dryers’ walls is negligible. The energy balance method is used to create the systems’ energy transfer equations for the active components. The energy balance method is described in Heat transfer, a practical approach (2002) by Yunus Cengel. (Yunus A. Cengel, 2002 pp. 272-276) The UV stabilized (µ) plastic cover tilted at 4.90 temperature model: Figure 3.02: Energy balance across Transverse cross-section of the drying chamber. Energy balance on cover; Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 29 ( ) The equation reduces to Thus, if The corrugated iron sheet bed temperature model: Energy balance on the iron sheet; And if the equation reduces to The working fluid/air stream (air flowing in & out of the drier) temperature model: Figure 3.03: Energy balance across longitudinal cross-section of the drying chamber. Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 30 The three equations describe the thermal behavior of the cover, air and drying bed surface in the heating chamber. Boundary (initial) conditions: At , , ambient air temperature. , measured initial cover temperature at the inlet. , measured initial iron sheet bed at the inlet. 4.2.4 Drying chamber model: Assumptions made: 1. Air flow is one dimensional, only along the axis of the dryers’ length. 2. All drying of the food is due to thermal energy and mass transfer. 3. No chemical reactions occur in the air or between the air and food. 4. Shrinkage of the pineapple is not considered. 5. Pineapple slices are uniform cylinders and air absorptivity is negligible. 6. The black walls absorb and re-radiate all the energy incident on them and the fraction of solar radiation lost through the dryers’ walls is negligible. 7. Drying computation is based on a thin layer drying model. 8. The iron sheet bed is covered by the product and thus receives little or insolation, therefore considered insignificant in the energy balance. Figure 3.04: Energy balance across transverse section of the drying chamber. Cover energy balance: Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 31 ( ) If Similarly to heating chamber, the equation reduces to; Mass balance: ; The exchange area is the product surface which cancels out; The product’s coefficient is negative since it is losing moisture, thus; ; Drying Product energy balance: If The exchange area is the product surface which cancels out; the equation re- duces to, Airstream energy balance: Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 32 The equation reduces to; Drying rate: The Newtonian drying model will be used to calculate moisture loss for the pineapple. The drying constant equations and equation constants for most crops (cereals, grains) using the page model are available from, (ASAE Standards D245.5, 1998). Drying equations have different forms and for given crops, some models are much more accurate. Most thermal and moisture models are empirical rather than theoretical, (Md. Rajibul Islam, 2010). Boundary (initial) conditions: The final conditions in the heating chamber become initial conditions for the drying chamber, thus At 4.2.5 Drying air properties: The incoming ambient air into the dryer is already humid, for the entire heating chamber, it assumed the humidity of the moist air doesn’t change, it starts to increase in the drying chamber as moisture is added to it. Thus the thermo conductivity, density and specific heat change as air temperature increases in the heating and drying chamber according to the equations below; Density of incoming atmospheric air; Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 33 Saturated vapor pressure, Pvs; (ANSI/ASAE, 1979 (R2005)) , Vapor pressure; Thus, Humidity ratio, w; ⁄ Density inside the dryer, ρa; Specific heat capacity of moist air using mass fractions, Ca; ( ) Viscosity, µ and Thermo conductivity, ka are assumed constant since their computation as they vary with absolute humidity is intensive and varies very slightly. Thus µ=1.8*10-5 Pa.s and ka=0.026W/mK 4.2.6 Heat transfer coefficients, constants and psychometrics: Radiative heat transfer coefficients: (Mudafer Kareem, 2011), (S. Sadodin, et al., 2011) (M A Hossain, et al., 2009). Convective heat transfer coefficients: , Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 34 . The coefficients depend on the instantaneous cover, iron sheet bed and food temperatures and are recomputed on every grid element. MC dry basis: The drying constant values K, were estimated from the experimental results since an equation for the drying constant of pineapple depending on RH, T and velocity was unavailable. For natural convection from 12:15 to around 3:30, average air temperature was beyond 400C, K was estimated to be 0.06h-1 beyond 4:00 air temperatures were lower and K was estimated to be 0.057h-1. For forced convection from 12:15 to around 3:30, average air temperature was beyond 350C, K was estimated to be 0.082h-1 beyond 4:00 air temperatures were lower and K was estimated to be 0.077h-1. Water activity, aw is got from (Akoy, et al. p. 3), it was formulated for mango slices but will be used to estimate that of pineapple slices in this study. ( ) me for pineapple can be got from the modified Oswin equation, (PHOUNGCHANDANG, et al., 2000 p. 991) and (ASAE Standards D245.5, 1998) Latent heat of vaporization of water from pineapple; (ANSI/ASAE, 1979 (R2005)) √ Specific Volume; ⁄ Variation of wind speed Vw with height above ground level on the cover, h; Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 35 Enthalpy of drying air can be approximated using the equation below: , for Cover properties: The cover is transparent polythene, Corrugated Iron bed properties: The bed is painted black in the heating chamber and burnished in the drying chamber, For the unpainted bed in the drying chamber; 5. The computer modeling /simulation of the orchard solar dryer: The flow of activities in developing the computer model is from, (Jerry Banks, 1999), (Jerry Banks, et al.), (Harry Perros, 2009), (Robert E. Shannon, 1998) and (Deborah A. Sadowski, et al., 1999). The essence or purpose of simulation modeling is to help the ultimate decision-maker solve a problem. The problem to be tackled is predicting performance and parameters of the orchard solar dryer; a mathematical model is developed and used in the proceeding steps to program a simulation model. Components of Computer model; 1. Computer algorithm, based on thorough system understanding. 2. Accompanying numerical data to build system processing/functioning. 5.1 Model Solution methodology: The solar dryer’s model has eight equations that cannot be solved analytically; this is because the system is transient not steady state. The equations are thus solved using the finite difference method to create a numerical simulation model of algebraic equations that can be programmed using MATLAB. This involves transforming from the physical to the computational domain using a one dimensional approach, generating difference equations using forward differences (numerical formulation) to create a Cartesian grid, using the initial boundary conditions to solve temperatures and other values for subsequent nodes. This is done for each mesh element on the grid sequentially. Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 36 5.2 Transformation of physical solar system to computational domain: The dryer is split in to small element using grid lines to create a finite element mesh. The model equations will be converted to finite difference equations. 5.2.1 Finite difference equation formulation for the entire dryer: The methods used are from (Yunus A. Cengel, 2002 pp. 269-272), (Ashish Kumar, 2009 pp. 13-15), (Rosarin Smitabhindu, 2008 pp. 18-24)and (Irudayaraj, 2002 pp. 7683). Consider the finite mesh of the computational domain of the entire solar dyer on the next page; Figure 3.05: Computational domain of the entire dryer. Heating chamber using forward finite differences: The three equations for the heating chamber and five equations for the heating chamber are discretized into difference equations that will be sequentially solved. The grid mesh spans the length of the entire collector, the grid spacing, as the position step. The values of Tc, Ta and Tb will be calculated at each node for the drying chamber and Tc, Ta, Tp, Mp, RH at each node of the drying chamber. The appropriate time step/interval Δt will be determined using sensitivity analysis; a value of 5s can used as a starting point. The simultaneous partial differential equations are going to be converted to simultaneous finite difference equations using the finite difference method. Finite differences of heat conduction are formulated by replacing the derivatives in the differential equations with differences. By replacing a differential time interval dt by a fiGulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 37 nite time interval of Δt, reasonably accurate results can be obtained by replacing differential quantities by sufficiently small differences For a general difference equation in finite difference formulation, the temperature is assumed to vary linearly between the nodes. The forward difference formula; , thus Heating Chamber Cover temperature: Heating Chamber Airflow temperature: Heating Chamber iron sheet (bed) temperature: ( ( ( ) ( ) ) ) Drying Chamber finite difference formulation: Drying chamber Cover temperature: This is similar to the one for the heating chamber, except that the iron sheet bed is replaced by the drying pineapple; ( Drying chamber mass balance; ) Humidity change; Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 38 Drying pineapple temperature: Drying air temperature: MC of pineapple: The Newton drying model will be used to describe the moisture loss of the pineapple, Differentiating m with respect to t; The average temperature of air in the two dryers was 36-41 and 41-450C respectively, Average thickness was 5-8mm Thus; 5.2.2 Pineapple Surface Area for moisture loss: The pineapple slices are assumed to be uniform thin cylinders of thickness a circle is widest at the center, Lpdt= √ , however sketch, lx=Δx Nodal pineapple moisture loss and heat transfer area. Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 39 5.2.3 Solar dryer performance analysis: From drying recovery equations, Mass of water removed from product Mw is given by; Mw Mi Drying Air flow: Considering the stack effect due to chimneys, Stack effect is the movement of air into and out of buildings, chimneys, flue gas stacks or other containers due to buoyancy created by the temperature difference between outside and air thus making air inside less dense. Due to natural convection from buoyancy: , this reduces to , (Ekechukwu O.V., et al., 1995) Airflow q (m3/s) due to natural convection, √ C is a discharge coefficient. For the orchard dryer, height of elevation Chimney height, √ . Thus ⁄ Air flow velocity due to natural convention, Va ⁄ The estimated velocity values are going to be used in the simulation model. Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 40 For higher temperatures v can go up to 0.07m/s. 5.2.4 Dryer Efficiency: Energy required to dry the product: Total energy the dryer absorbs during the drying time: Heating chamber efficiency: Drying chamber efficiency: Drying efficiency (efficiency of the entire dryer); , If a solar panel is not used, Quantity of air needed to dry the pineapple (absorb Mw kg of water): Required (minimum) air flow rate: Drying Rate: DR = Figure 3.06: Gross and Net efficiency of a typical air collector vs. Air flow rate, (Werner Weiss, et al. p. 71). Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 41 The air flow rate required for proper drying depends on the product to be dried, the moisture content of the product, the available solar radiation and the dimension of the dryer. 5.3 Model Translation. This involves formulating an algorithm to solve mathematical mode then programing the algorithm in MATLAB. The algorithm is basically the finite difference equations which will be solved for every Δx along the dryer length. This is split into the flowing respective phases; Input Data preparation, verification and finally validation. Identifying and collecting the input data needed by the model. The required meteorological data and drying parameters for pineapple are prepared. Verification; This involves confirming that the model operates the way it is intended (debugging) and that the output of the model is realistic and representative of the output of the solar dryer. The model should run without bottlenecks and unreal (complex number) output, this is achieved by appropriate exception handling. The fruit considered for validation is pineapple due to it’s relative availability, suitability for drying and relative ease of preparation for drying. Results from drying of pineapple in the dryer were compared to results from the model for similar conditions. 5.3.1 Validation; Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 42 The data from the dryer’s simulation was plotted and analyzed against the data from physical experimentation to see the level of agreement. This was done using pineapples. Figure 3.07: Flowchart for Model Solving algorithm: Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 43 5.3.2 Model solving pseudo code algorithm: assign constants values; ie(g=9.81, sigma etc) assign values to pineapple, cover and iron sheet bed properties create matrices representing variation of RH, E(insolation), wind speed and ambient air temperature for the entire drying time dx=1/1000 or 2/1000 or 5/1000, 10/1000; dt=5,10,15,30 0r 60 seconds; depending on available computing resources for the entire drying time in dt intervals pick current RH, E, Vw and Tam from matrix for the entire drying chamber in dx intervals calculate w, new air shc,Pa calculate Re, Pr, Ra the Nu calculate current heat transfer coefficients calculate bed, cover and air temp calculate the absorbed heat energy and sum it up in a summing variable log results to results matrix end calculate the instantaneous efficiency of the heating chamber for each mesh for each row in the mesh (in dx intervals) calculate pineapple shc and density based on its current temperature calculate current air density and shc pick a K value %an equation was not available calculate the new latent heat of pineapple calculate the new mc of the slice section calculate new RH and mass of water lost and add it to summing variable calculate Re Ra, Pr then heat transfer coefficients calculate new Ta, Tp and Tc calculate w, air enthalpy and heat absorbed by pineapple, add this to a summing variable log results to results matrix end calculate the mesh’ drying rate end calculate the entire dryer’s drying rate end calculate the instantaneous efficiency of the drying chamber for any distance of unloaded drying chamber repeat the calculations to calculate Ta, Tb, Tc, rh, h, w, Pa,Vs end calculate the overall drying and heating chamber efficiency Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 44 5.3 Pineapple: Pineapple (Ananas cosmosus) is a perennial tropical fruit belonging to the Bromeliaceae family. In it’s family, it is the most edible and thus most economically vital. It grows on the ground and can grow up to 1m tall and 1.5m wide. Fresh pineapple fruit on average contains 86% water, carbohydrates, sugars, vitamins A, C and carotene, beta and low amounts of protein, fat, ash and fiber. Figure 3.08: Table of physical properties of pineapple Property Value Average fresh MC 85-87% Diameter (Experimental) 10cm-slice, 11cm fresh Length (Experimental) 15-17cm Fresh slice Density Approx. 1100kg/m3 Fresh Specific heat Capacity 3.43 J/gK sliced, 3.68 J/gK fresh, function of T and m Latent Heat of Vaporization Reflectance 0.2 Absorbance 0.8 Emittance 0.9 Drying Constant, K Given in model script, depends on RH, v and T Fresh fruit Temperature (Experimental) 22-240C Figure 3.09: Optimum conditions for solar drying of quality pineapple Property Value Air temperature 50-600C Relative humidity of flowing air <30% Air velocity, (air mass flow rate) Higher air mass flow rates are better Thickness of slices <10mm Maximum Drying air Temperature 650C Various cultivars of pineapple exist; the one common in Gulu is Smooth Cayenne. J. L. Woods and Phoungchandang S in their 2000 article reported an average value of 0.80 for the absorptivity and 0.9 for long-wave emissivity for bananas. If the transmittance of pineapple can be taken as 0 since it is opaque and thus reflectance is 0.2. These values can be a good estimate to pineapples and will be used, (PHOUNGCHANDANG, et al., 2000). These properties are used in mass and heat transfer calculations during the drying process. Dried pineapples have an average MC of 11-13%, 600C is the optimum drying temperature for most fruits. (B.K. Bala and S.Janjai) Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 45 5.3.1 Pineapple density and specific heat: Fresh pineapple on average contains 86%, 12.63% carbohydrate, 0.22% ash, 0.54% protein, 0.12% fat by weight as main constituents and the rest being vitamins and minerals with ascorbic acid have the highest percentage among the vitamins. During drying it can be assumed that only moisture is removed, thus the constituents of pineapple change as dries. This can be used to estimate the specific heat capacity and density of the pineapple as it dries based on the changing constitute percentage and pineapple temperature. The s.h.c of a food is given by (Joseph Irudayaraj, 2002 p. 18), as The values depend on pineapple temperature; Water, Protein, Carbohydrate, Ash, Fat, The density of a food is given by (Joseph Irudayaraj, 2002 p. 21) as ⁄ ⁄ Water, Carbohydrate, Protein, Ash, Fat, ⁄ 5.4 Dryer optimization: To optimize the dryer, two parameters, the air velocity and the thickness of the fresh pineapple will be varied in a script that simulates pineapple drying form an MC of 86% to 12.2807%wb, (614.2857% to 14%db). The velocity is varied from 0.06(natural convection), 0.15 to 2m/s as in the matrix below. Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 46 [0.1, 0.15, 0.5:0.5:2] This is a total of 6 sequential experimental simulations from v=0.1 to 2m/s with a constant thickness 4mm. After each simulation, the efficiency of the dryer and time taken to dry will be stored. After all the experiments are simulated, a graph of efficiency Vs air velocity, time to finish drying, drying curves and variation of average air temperature with distance in the entire dryer will be plotted. An optimal value can now be concluded. To get the optimal thickness of drying pineapple, the optimal velocity got from the simulation is fixed and the thickness is varied from 10mm to 2mm as in the matrix below [0.002:0.002:0.01]. This is total of 5 sequential simulations for thickness incrementing by a 2mm up to 10mm, similar graphs will be plotted and an optimal value concluded. 5.4.1 Optimization script pseudo code algorithm; v=[matrix of velocity to be used in each experiment] zp=[matrix of pineapple thickness to be used in each experiment] for all required experiments% size of velocity or thickness matrix clear memory pick a velocity or thickness to run entire simulation while the pineapple moisture content is less than required pick current RH E, Vw and Tam for the entire drying chamber in dx intervals calculate w, new air s.h.c Pa calculate Re Pr, Ra the Nu calculate current heat transfer coefficients calculate bed, cover and air temp calculate the absorbed heat energy and sum it up in a summing variable log results to results matrix end calculate the instantaneous efficiency of the heating chamber for the entire drying chamber in dx inter for each mesh for each row in the mesh (in dx intervals) calculate pineapple shc and density based on its current temperature calculate current air density and s.h.c pick a K value %an equation was not available calculate the new latent heat of pineapple calculate the new mc of the slice section calculate new RH and mass of water lost and add it to summing variable calculate Re Ra, Pr then heat transfer cofficients caculate new Ta, Tp and Tc calculate w, air enthalpy and heat absorbed by pineapple, add this to a summing variable log results to results matrix end end calculate the mesh drying rate end calculate the instantaneous efficiency of the drying chamber for any distance of unloaded drying chamber repeat the calculations to calculate Ta Tb Tc, rh, h, w, Pa,Vs end end calculate the drying and heating chamber efficiency and log results to a file log all results to a file end The values of the drying constant for higher velocities is unknown since no equation to predict K depending on RH, product temp and velocity for pineapple or a similar fruits is current unknown and thus unavailable to the author. The drying constants used were estimated from experimental data only for natural convection and an estimated velocity of 0.2 to 0.3m/s by 2 DC fans. Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 47 6. EXPERIMENTATION; 6.1 Dryer renovation:     The dryer’s exterior was painted grey and the interior painted black The insulation of the heating chamber was improved using papyrus under the iron sheet bed and the biomass gap was covered to reduce heat loss. The chimneys were replaced with new ones and wooden stands were created to stabilize the chimney in case of rain and wind. The interior and cover were cleaned and the insect netting was replaced. The experimentation was performed in Gulu University in Laroo division of Gulu town in Uganda, an East African Country on Saturday 26th May 2012, located at 02 47 24N, 32 19 01E (Latitude:2.7900; Longitude:32.3170). Due to unforeseen circumstances, the drying began from 12:15 to 17:35. Seven pineapples were sorted right from the market the day before in order to pick only ripe, acceptable and undamaged pineapples. The pineapples were then washed and peeled. The peeled pineapple was then transversely cut in to half cylindrical slices of 5mm. This slices were loaded into the drying meshes, 3 pineapples per tray making the experiment require six pineapples for the two drying meshes. Due to inaccuracy caused by using knives to cut, the thickness of the slices varied between 5 to 10mm. Average diameter was 10cm. Each tray received 80 half slices of pineapple. During drying the pineapples undergo non-enzymatic browning but for this study the browning will not be controlled due to technical and economic constraints. B. K. Bala reduced this browning during the drying and storage by treating 1Kg of fresh fruits with 40mg of sulfur burnt to sulfur dioxide, (B.K. Bala and S.Janjai). Dry pineapple x-tics: Max m=18%, Aw=0.55-0.65 at 200C Figure 3.10: Fresh pineapple slices loaded on a drying mesh. Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 48 Figure 3.11: DC fans blowing air over drying sliced pineapple. Equipment/Instrumentation used to collect the drying data and parameters: All of the weather data was got from the newly installed weather station in the Biosystems department. Any other data required was measured if possible or estimated using reference parameters. A class III digital weighing apparatus, Scasen BS 600RD (± 0.1 g accuracy) measures the mass loss of the product during the drying process. During each drying experiment, mass of the pineapple 3 pineapple slices along each drying line on the mesh was measured by removing a slice from the drying chamber for approximately 5-10s. The average of these 3 values was taken as the currents slice mass for that drying line. The mass and temperature values were recorded initially for each 10minutes for the first 40minutes of drying, then each 20 min for the next 40minutes then for each 30minutes hour. An ordinary thermometer measured the temperature of the pineapple as the mass was being taken. 6.2 Photovoltaic fan system installation: To improve the air flow of the dryer so as to increase the evaporation rate thus drying efficacy of the dryer, 3 axial DC fans were installed just above the biomass chamber. The success achieved by natural convection solar dryers has been limited due to low buoyancy induced air flow, (Bala, et al., 2009) The system requires no battery since food is only dried when there is enough insolation, this insolation can also be used to directly power the fans. The solar insolation automatically controls the airflow, the hotter it is, the higher the airflow and the reverse is true. Each fan has diameter of 11cm and requires 12V to run and 7.5V to startup. Each fan can produce a maximum air flow rate of 0.05m3/s increasing the air speed by about 0.15m/s. The 3 fans can produce 0.15m3/s increasing the air velocity by 0.45m/s. Since the system relies on insolation to provide power, the power output varies with solar intensity. Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 49 Figure 3.12: Operating characteristics of the Fifara FD1238D12HS DC fan. Property Value Rated Voltage 12V Operating Current 0.58A Operating voltage 10.5-13.5V Starting voltage, Direction of Rotation 7.5V, Counter-clockwise with 7 blades Revolutions per minute (rpm) 2850 ±10% 0 Dimensions, Life at 25 C 11x11x3.8cm, 30,000hrs Operating Temperature Range 20-800C Operating Humidity Range 20-80% Air flow rate 0.04964m3/s, approx. 50liters per second Noise level, weight 42.8dB, 230g Figure 3.13: Solar panel layout to drive fans. Figure 3.14: Circuit Layout of solar fan system. I The Fifara FD1238D12HS DC fan is basically used to cool heavy electronic equipment like amplifiers and servers. It was chosen due to the dimensional constraints of the dryer, the finance available, it’s good airflow rate and ability to work in highly humid environments. The three fans are connected in parallel since they used the same voltage that the panel can provide. Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 50 CHAPTER IV 7. RESULTS AND DISCUSSIONS The drying was done from 12:15pm to 17:35pm. The data below was got from the Campbell weather station at the Biosystems Engineering Department. The weather station is about 250m from the solar dryer, thus the data is a valid representation of the weather conditions at the drying site. Figure 4.01: Spread Sheet showing hourly variation of weather on 26th/05/2012 TIMESTAMP Tam RH Vw E Pa Tdp Rain ρa TS, 5/26/2012 0 % m/s W/m2 Pa 0 mm Kg/m3 4:00 5:00 6:00 7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 Drying average C 16.75 16.8 17.06 17.06 18.65 21.5 23.23 25.02 26.3 27.16 27.55 27.92 28.38 28.38 27.99 25.47 22.55 20.73 27.6686 95.2 94.6 92.4 91.1 80.9 77.35 73.04 74.22 62.49 58.31 54.12 47.77 44.31 52.68 52.4 78.67 79.08 77.8 1.16 1.043 1.334 0.988 0.749 1.646 1.684 1.557 1.867 1.631 1.228 2.046 2.136 2.064 1.315 0.891 0.818 1.329 0 0 0 5.687 131.9 352.5 519 670.5 749.9 796.3 586.3 693.2 621.9 453.3 243 63.49 0.038 0 C 89100 89100 89100 89100 89100 89200 89200 89200 89200 89200 89100 89000 88900 88900 88900 88900 89000 89100 89050 15.91 15.87 15.81 15.8 16.51 17.5 18.64 19.55 19.03 18.58 17.67 17 15.98 16.26 16.68 18.4 18.65 16.81 17.42 0 0 0 0 0.254 0 0 0 0 0 0 0 0 0 0 0 0 0 1.070598668 1.070414057 1.069455103 1.069455103 1.063627908 1.054522524 1.048367377 1.042073939 1.037619739 1.034648398 1.032148116 1.029722708 1.026996636 1.026996636 1.028326634 1.037004205 1.048422146 1.056100105 Figure 4.02: Insolation (E) from 4:00 to 21:00 on 26th/05/2012: Insolation, E on 26/05/2012 900 800 700 W/m2 600 500 400 300 200 100 0 4:00 5:00 6:00 7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 Time Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 51 Figure 4.03: Insolation during drying: Insolation W/m2, 12:15 to 17:35 800 700 W/m2 600 500 400 300 200 12:00 13:00 14:00 15:00 Time 16:00 17:00 18:00 Figure 4.04: Wind speed and RH from 12:15 to 17:35 Relative humidity Wind speed 2.2 65 2 60 1.6 55 % m/s 1.8 50 1.4 1.2 1 12:00 13:00 14:00 15:00 16:00 17:00 18:00 Time 45 40 12:00 13:00 14:00 15:00 Time 16:00 17:00 The average dew point temperature was 17.3140C for the drying period. 7.1 Analysis and Interpretation. An excel spreadsheet was created to continuously calculate moisture content from mass lost for the entire drying operation. The spreadsheet is on the next page. Average moisture lost during peeling is 54g; average mass of the peeled pineapple was 1,330g, The average mass of a fresh pineapple slice was 24.5g, the pineapple slices were kept overnight due to weather conditions and time. On Saturday, morning before drying the average mass was 24.3g, Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 52 18:00 Drying commenced at 12:15pm, In the fan assisted dryer, the average drying temperature was between 36-380C, in the control dryer, the average temperature was between 45-470C. ⁄ ⁄ Figure 4.04: Experimental Moisture Content Spreadsheet of a half pineapple slice. Time Fan Cont Fan Cont Fan Cont Mw,f Mw,c E, avg 2 EJ,Fan Ej, (Ct) min Hrs M(g) (g) wb wb g g W/m J J 0 0 24.3 24.3 0.8528 0.8528 5.7935 5.7935 0 0 761.5 0 0 db db 10 0.2 24 24.1 0.85096 0.85158 5.7096 5.7376 0.3 0.2 769.23 57942.29 38322.8139 20 0.3 23.6 23.9 0.84843 0.85034 5.5978 5.6817 0.4 0.2 776.97 77256.38 38322.8139 5.6257 0.4 0.2 784.7 77256.38 38322.8139 5.3462 5.5419 0.5 0.3 792.43 96570.48 57484.2208 30 0.5 23.2 23.7 0.84582 0.84907 40 0.7 22.7 23.4 0.84242 0.84714 5.486 60 1 21.5 22.4 0.83363 0.84031 5.0107 5.2623 1.2 1 743.8 231769.2 191614.069 80 1.3 20.3 21.4 0.8238 0.83285 4.6752 4.9827 1.2 1 673.8 231769.2 191614.069 110 1.8 18.8 20.2 0.80974 0.82292 4.2559 4.6473 1.5 1.2 595.21 289711.4 229936.883 140 2.3 17.4 18.9 0.79443 0.81074 3.8645 4.2838 1.4 1.3 648.66 270397.3 249098.29 170 2.8 16.3 17.9 0.78055 0.80017 3.5569 4.0042 1.1 1 687.26 212455.1 191614.069 200 3.3 15.5 17.1 0.76923 0.79082 3.3333 3.7806 0.8 0.8 651.61 154512.8 153291.256 230 3.8 14.8 16.5 0.75831 0.78321 3.1376 3.6129 0.7 0.6 607.03 135198.7 114968.442 260 4.3 14.2 16 0.7481 0.77644 2.9699 3.4731 0.6 0.5 523.18 115884.6 95807.0347 290 4.8 13.6 15.5 0.73699 0.76923 2.8021 3.3333 0.6 0.5 435.78 115884.6 95807.0347 320 5.3 13 15 0.72485 0.76154 2.6344 3.1935 0.6 0.5 330.63 115884.6 95807.0347 11.3 9.3 2182493 1782010.85 Tota l M Figure 4.05: Simulated Moisture Content of a half pineapple slice Time min Hrs Fan Cont Fan Cont Fan Cont Mw,f Mw,c E, avg M(Kg) (Kg) wb wb db db g g 0 0 0.0243 0.0243 0.8528 0.8528 10 0.2 0.0238 0.02394 0.84993 0.850586 5.793 5.7935 5.664 5.6928 20 0.3 0.0233 0.02355 0.84672 0.848093 5.524 30 0.5 0.0228 0.02316 0.84325 0.845566 40 0.7 0.0223 0.02278 0.8397 0.843005 5.38 5.4753 5.238 5.3696 60 1 0.0213 0.02205 0.83241 0.83778 80 1.3 0.0205 0.02134 0.82522 0.832416 110 1.8 0.0192 0.02034 0.81417 0.824114 140 2.3 0.0181 0.01939 0.80261 0.815503 170 2.8 0.0171 0.01849 0.79035 0.806574 200 3.3 0.0161 0.01765 0.77756 0.797328 230 3.8 0.0152 0.01685 0.76444 0.787768 260 4.3 0.0144 0.01611 0.75086 0.73687 0.777914 0.76779 290 4.8 0.0136 0.0154 320 5.3 0.0129 0.01475 0.72247 0.757537 Total M 5.583 0 0 W/m 2 761.5 0.464 0.36 769.2 0.5 0.393 0.516 0.385 777 784.7 0.505 0.378 792.4 4.967 5.1645 4.721 4.9672 0.971 0.734 743.8 0.879 0.706 673.8 4.381 4.6855 4.066 4.4201 1.217 1.007 595.2 3.77 4.1699 3.496 3.9341 1.127 0.949 1.06 648.7 0.895 687.3 0.981 0.844 651.6 3.245 3.7118 3.014 3.5028 0.895 0.795 607 0.828 0.748 523.2 2.8 3.3064 2.603 3.1243 0.764 0.702 435.8 0.705 0.651 330.6 11.41 9.547 Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 53 Figure 4.06; Modeled and experimental natural convection drying curve, wet basis from 12:15 to 17:35: 0.85 MC, wb 0.83 0.81 Exp Cont wb 0.79 Model Cont wb 0.77 0.75 0 10 20 30 40 60 80 110 140 170 200 230 260 290 320 Drying time, min Figure 4.07; Modeled and experimental natural convection drying curve, dry basis from 12:15 to 17:35: 6 MC, wb 5 Exp Cont wb 4 Model Control wb 3 0 10 20 30 40 60 80 110 140 Drying time, min 170 200 230 260 290 Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 54 320 Figure 4.08; Modeled and experimental forced convection drying curve, wet basis from 12:15 to 17:35: 0.86 0.84 0.82 0.8 Experiment 0.78 Model 0.76 0.74 0.72 0 10 20 30 40 60 80 110 140 170 200 230 260 290 320 Figure 4.09; Modeled and experimental forced convection drying curve, dry basis from 12:15 to 17:35: 6 5.5 5 4.5 4 Experiment 3.5 Model 3 2.5 0 10 20 30 40 60 80 110 140 170 200 230 260 Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 55 290 320 Figure 4.11: Modeled Natural Convection drying conditions in the dryer from 12:15 to 17:35; Figure 4.10: Modeled Instantaneous drying rate for one drying mesh of pineapple; Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 56 Figure 4.12: Modeled pineapple temperature with time. Figure 4.13: Modeled Temperature distribution in an unloaded dryer under natural convection with E=750W/m2, v=0.07m/s and RH=0.61445. Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 57 Figure 4.14: Modeled w, specific volume and air density in the dryer, RH=0.61445. Figure 4.15: Modeled Air enthalpy in the empty dryer RH=0.61445, v=0.056, E=750; Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 58 √ ∑ From the spreadsheets, RMSE was calculated to be 0.0940943 db for 25 data points, R= 0.996662134 and R2=0.9933 √⌈ Efficiency; ∑ ∑ ∑ ∑ ∑ ∑ ∑ ⌉ The air velocity during experimentation was not measured and it is required to calculate heating chamber efficiency. 7.1.1 Natural Convection; The heating chamber was 14% efficient from the model; experimentally the drying chamber was estimated to be 4.3% efficient and from the model 4%. 7.1.2 Forced Convection; The heating chamber was 19% efficient from the model; experimentally the drying chamber was estimated to be 6.4% efficient and from the model 5.9% efficient. 7.2 Model Sensitivity Analysis; Position steps of 1, 2,5mm calculate the temperature, RH, w, h, Vs, Pa distribution along the entire dryer with good accuracy. 10mm has a low accuracy and generally produces smaller values. Time steps of 5,10,15,30 and 60 seconds can be used with good accuracy. Change in RH has no significant effect on predicted temperatures except but higher RH values give bigger air enthalpy and humidity ratio. The K values are not derived from equations, but from drying experimentation estimates. Pineapple temperature decreases with insolation. For drying simulation the most appropriate position step is 2mm. 7.3 Computer/Computational requirements: It required an average of 20 to 22 seconds to execute fully on Pentium Dual Core E5700 with 2GB DRR3 RAM using a time step of 60 seconds and a position step of 2mm to simulate 5.33hours of actual drying from 12:15 to 17:35 on 26th/05/2012. A smaller time step doubles the memory required and computation time. Each value occupies 8 bytes of memory. A typical results matrix is [time, distance] for 5hours using a 60second time step, [300 4540], having 1362000 values. 1362000 values occupy 1362000*8/(10242)=10.4MB . However, this is just one 5 hour result, about 10 (2 dimensional) results are required (w, mcwb, mcdb, pa, s.h.c, Pp., Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 59 Vs., Ta, Tc, Tb, RH, M, etc. (depends on what you want to log)) and 4 one dimensional results DR, 3 efficiencies. These altogether require at least 150MB of free RAM. Using a smaller time step and position step increases the memory requirement in multiples of 2 and computation time accordingly. If a time step of 5 seconds is used to simulate 5hours of drying for a 9m long dryer using a position step of 2mm, 10*[3600 4500] +4*[1:3600] floating point variables are required. This require 1.236Gb of RAM for 5hour drying, 20hour drying will require 4.944GB which is only available on high end systems, grids or servers. This will force MATLAB to use virtual memory from a page/swap file on the hard disk causing tremendous slowdown in system performance and response since hard drives are much slower than RAM and cannot effectively handle the great RAM-CPU memory controller bandwidth. Otherwise a computer runs out of memory and MATLAB returns an out of memory error exit code. The advantage is the result matrices are created before the drying loop, so an error is got early and values adjusted according to the available hardware. All in all, 60 seconds and 2mm are the most accurately economical increment steps. Figure 4.16: Table of Summarized Gulu University Orchard Solar Dryer properties: Property Value Dryer Type Cover Area, Average cross-sectional area Length, width and height above ground Product loading capacity Chimney length, chimney area Hydraulic Diameter Cover Absorber Hybrid solar tunnel with biomass option 10.8912m2, 0.3309m2 9.08m, 1.2m, 0.58 to 1.5m. 6x0.832m2 (6 meshes) 3x1m, 3x m2 0.42m Transparent HDPE Iron sheet painted black in heating chamber, burnished in drying chamber 2.80,00 and 70 for dryer, 50 cover Flat plate Papyrus mats for the absorber and wooden sides. 0.03-0.07m/s 14% 5% 95-65g/hr. 45-650C 25-27hrs (some pineapple browns) 0.2-0.45m/s 19% 7% 130-78g/hr. Tilt angle Collector type Insulation Estimated average Air velocity (Natural convection) Est. Heating Chamber Efficiency (Natural Convection) Est. Drying Chamber Efficiency (Natural Convection Est. Drying rate 1st mesh (Natural convection) Drying chamber temp range (entrance –exit) Nat Conv. Est. Drying time pineapple (6.143 to 0.15db) Nat Conv. Estimated average Air velocity (2-3 fans) Est. Heating Chamber Efficiency (Natural Convection) Est. Drying Chamber Efficiency fans Est. Drying rate 1st mesh fanned Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 60 Drying chamber temp range (entrance –exit) fanned Est. Drying time pineapple (6.143 to 0.15db) fanned DC fan power required for full capacity (0.15m3/s) 36-470C 18-22hrs (pineapple remains yellow) 40W CHAPTER V 8. CONCLUSIONS; 8.1 Concluding remarks from experimentation and computer model results comparison;  The model developed satisfactorily agreed with experimental results having a RMSE of 0.094 db and R2 of 0.9933 and thus can be used to predict drying time, efficiency and many operational and psychometric parameters.  From the model and physical experimentation, forced convection/mixed drying outperforms natural convection with higher drying rates, efficiency and thus greatly reduces drying time that natural convection requires.  The pineapple dried using forced convection does not brown due to lower drying air temperatures (35 to 450C) as compared to natural convection (45 to 650C).  From the computer model, a lot of new relationships and variables can be predicted by varying ambient conditions and dryer characteristics, making it a very powerful tool in design and performance evaluation/estimation of solar dryers/heaters. 8.2 Recommendations; 1. More computer models should be developed in areas of thermodynamics, fluid mechanics, hydrology and meteorology, drying and air conditioning of agricultural products and any other applicable courses to give a deeper insight and predict outcomes or requirements. 2. More research on performance/design of solar dryers/heaters/systems based on computer aided engineering tools backed by physical experiments should be carried out. 3. Equipment and tools used in thermodynamics, fluid mechanics, control systems and small scale agro processing like a slicer, anemometer, thermocouple, RH meters, data units and other appropriate tools should be availed. 4. Future research should establish a relationship between the drying constant K, RH, product/air temperature and air flow velocity for pineapple or similar fruits. 5. Future solar dryers should be constructed without air leaks and gaps and physical properties of the materials used must be got as they are being bought. Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 61 6. A data acquisition system for physical equipment should be setup to ease the data collection process, greatly improve accuracy and increase the number of experiments run. 7. A better solar dryer be constructed at the new Biosystems site. 8. For the dryer used in this study, the cover should be replaced. 8.3 Project Cost Spreadsheet: Table 5.01: Project Cost Spreadsheet. COST (Ugx) Solar fan system Amorphous Photovoltaic module 10W,12V (90x30cm) 3 (12V,1.1A,11cm diamter) QuietDC fans (18,000 each) Thin Low Resistance Wiring (20m) @700 per meter 3 Portable Switches,Packet of Wire Clippers and Pins Experimentation, and Renovation Insect and Dust netting(1.5m) 4" grey PVC Pipe (6m long) for replacing worn out chimneys 7 Pineapples @ 2,000 110,000 54,000 14000 18000 44 21.6 5.6 7.2 13,000 23,000 14,000 5.2 9.2 5.6 10,000 3,500 3,000 35000 25,000 80,000 4 1.4 1.2 14 10 32 56,000 458,500 22.4 183.4 Papyrus mats (4x(1.5x2m2)), @2,500 each 6 Plastic caps to seal each chimney 1(0.5+0.5) kg of (1.5", 2") common woods Nails Oil gloss Paint(1.5L Black and 2L Grey) @10,000 per L Transportation 12 Skilled Carpenter hours (2x6hrs) Publishing 4 hard cover copies of this report Total Cost NB: At the time 1$=2,500Ugx COST(US $) APPENDIX 1: Computer model MATLAB Script / Algorithm. %GULU UNIVERSITY; SOLAR DRYER HEATING AND DRYING MODEL %circular slices of pineapple loaded in rows in drying meshes %By OBIRA DANIEL 4th year Biosystems Engineering project, %SUPERVISED BY ENG. BEN EBANGU ORARI AND PROF. YUN SOL CHOL clear tstart=clock; tcpu=cputime; tic; %parameters to estimate required processor time dx=2/1000; dt=60; dtd=dt/3600; dxm=1000*dx; Time=19200/dt; b=100/dxm; %time step in hours and dryer distance in position steps %______________________Physical constants declaration_______________________ sigma=5.667e-8; g=9.81; R=287.07; %________FUNDAMENTAL OPERATIONAL PARAMTERS________ zp=5/1000; mo=5.793478261; %v=0.056; %Airflow velocity m/s,pineapple thickness m,inital product mc db (decimal) %___________________physical properties of the dryer collector/input values____________________________ angd=(2.8*pi/180); angc=(4.8*pi/180); W=1.22; zin=0.02;H=0.24; Hh=0.02;angb=(28*pi/180); %E=750; %______________________ Calculated dimensional properties of the dryer's collector________________________ h=H-Hh;w=W-2*zin; lc=W/cos(angc); %Adh=(Hh*w/2)+h*w+(((tan(angc))*w^2)/4);%transvere cross-sectional length of collector, m lb=w/cos(angb); Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 62 %_________________corrugated drying bed properties_________ refbed=0.1;absbed=0.8;emitbed=0.9;anglebd=2*(90-angb);kpy=0.029;zpy=7/1000; absbedburn=0.75;refbedburn=0.25;emitbedburn=0.23; %_________________cover physical properties_________ abscov=0.08;trscov=0.8;emitcov=0.8; Hd=H-(Hh/2)+(W/4)*sin(angc)+0.01;%average distance between cover and drying bed, m %____________Calcalation of any constant terms_________________________________ Ac=lc*dx;Ab=lb*dx; Ahc=0.3191; Ad=0.3309; %avg crosssectional area of the dryer, m^2 % Hdb=4*Adh/(lb+(2*h)+lc); %hydraulic diameter, m Ach=W*3.05; %______________WEATHER DATA ON SAT-25/05/2012 FROM 12:15PM TO 5:35PM in dt intervals_________________________ Eh=[linspace(761.5,796.3,2700/dt),linspace(796.3,586.3,3600/dt),linspace(586.3,693.2,3600/dt),linspace(693.2,621.9,3600/dt),linspace(621.9,453 .3,3600/dt),linspace(453.3,243,2100/dt)]; %Relative humidity of ambient air, decimal RH=[linspace(0.61445,0.5831,2700/dt),linspace(0.5831,0.5412,3600/dt),linspace(0.5412,0.4777,3600/dt),linspace(0.4777,0.4431,3600/dt),linspac e(0.4431,0.5268,3600/dt),linspace(0.5268,0.525166,2100/dt)]; %Atmospric pressure, Pa Patmall=[89200*ones(1,2700/dt),linspace(89200,89100,3600/dt),linspace(89100,89000,3600/dt),linspace(89000,88900,3600/dt),88900*ones(1,57 00/dt)]; %Ambient temperature, Celcius Tamc=[linspace(26.515,27.16,2700/dt),linspace(27.16,27.55,3600/dt),linspace(27.55,27.92,3600/dt),linspace(27.92,28.38,3600/dt),28.38*ones(1,3 600/dt),linspace(28.38,27.99,2100/dt)]; TamK=Tamc+273.16; %wind speed, m/s vwk=[linspace(1.808,1.631,2700/dt),linspace(1.631,1.228,3600/dt),linspace(1.228,2.046,3600/dt),linspace(2.046,2.136,3600/dt),linspace(2.136,2. 064,3600/dt),linspace(2.064,1.627,2100/dt)]; %____________INITIAL PRODUCT PROPERTIES___________ Tp=24+273.16; Mi=0.0243*2; Cwl=4186;Cwv=1872.3;d=10/100;r=d/2; nr=8; nc=5;nt=nc*nr; %initial pdt temp,avg slice mass, water shc,slice per row, no of rows, tot no of slices Apt=nt*pi*r^2;Aps=pi*d*zp*nt;Aptr=nr*pi*r^2;Dp=0.23; %top surface are of pineapple,side surface area, surface are per row, cover-pineapple avg distance for first two meshes. refpdt=0.2;abspdt=0.8; emitpdt=0.9; %pineapple reflectance, absorbance and emittance Tl=0.8;Tw=1.04; Tth=5/100;Tht=2.5/100;Amt=Tl*Tw;%Mesh length, width, height and area used for dying %_________initialising ones results matrices for required variables________ l=9.08; n=length(dx:dx:l); % Pvv=ones(Time,(n+1)); Pvvs=ones(Time,(n+1)); Tcc=ones(Time,(n+1)); Tbb=ones(Time,(n+1)); Taa=ones(Time,(n+1)); rhr=ones(Time,(n+1)); wh=ones(Time,(n+1)); ha=ones(Time,n+1); Tppd=ones(Time,nc); Pppd=ones(Time,nc); Cppd=ones(Time,nc); mpd=ones(Time,nc); M=ones(Time,nc); DR=ones(Time,nc); Vss=ones(Time,(n+1)); px=ones(Time,n+1); mpdwb=ones(Time,nc); Ndc=ones(1,Time); Nhc=ones(1,Time); Nsd=ones(1,Time); %efficiency matrices %____________________________constant terms used in the looping____________ Cons=cos(angd)*cos(angc);Cons7=cos(7*pi/180)*cos(4.9*pi/180); raconstant=cos(angd); Tppd(1,:)=Tp; mpd(1,:)=mo; M(1,:)=Mi; Tr=kpy/zpy; mpdwb(1,:)=mo/(mo+1); kx=length(dx:dx:3.05);Mwlt=0;Dra=ones(1,Time);dra=ones(1,Time); drytimes=0; Qevtt=0;Edc=0; Ehc=0; Qairt=0; Etot=0;%drying time (s) and total experimental heat energy mweu=1.8e-5; ka=0.026;vu=0;Ct=cos(7*pi/180); t=19200/dt;%drying simulation time in second dt intervals for T=1:t %loop for entire drying period vw=vwk(T); E=Eh(T);rh=RH(T); if E>500 v=0.056; %average speed in the entire dryer due to two fans running at varying insolation is 0.2 to 0.4m/s, V=0.04-0.07m/s for natural connvection else v=0.03; %average speed in the entire dryer due to two fans running at low insolation is 0.1-.15m/s, V=0.03m/s for natural convection end Rad1=abscov*(1+(Ab*trscov*refbed/Ac))*E*Cons; Rad2=E*Cons*(trscov*absbed)/(1-(1-absbed)*refbed); Tam=TamK(T); Ta=Tam;Tsk=0.0552*Tam^1.5;TT=Tsk^2;Py=Tam*Tr;Patm=Patmall(T); lxx=0;Tc=30+273.16;Tb=47+273.16; rhr(T,1)=rh; CO=(-27405.526+97.5413*Ta-0.146244*Ta^2+0.12558*(10^-3)*Ta^3-0.48502*(10^-7)*Ta^4)/(4.34903*Ta-0.39381*10^(-2)*Ta^2 ); Pvs=22105649.25*exp(CO); %Saturated vapour pressure, Pa Pv=rh*Pvs; %vapour pressure of air in the heating chamber w=0.6219*Pv/(Patm-Pv); %initial Humidity ratio of air in the heating chamber, wh(T,1)=w;Tcc(T,1)=Tc; Tbb(T,1)=Tb; Taa(T,1)=Ta; Pa=(Patm*(1+w)/(461.56*(w+0.62198)*Ta) ); px(T,1)=Pa; Vss(T,1)=(287.07*Ta*(1+1.608*w))/Patm; qair=0; ha(T,1)=1006.9254*(Ta-273.16)+w*(2512131.0+1552.4*(Ta-273.16)); for k=1:kx %calculation of air properties since they vary with temperature; lxx=lxx+dx; Ti=Ta; lcc=(lxx*lb/(2*(lb+lxx))); Pa=(Patm*(1+w)/(461.56*(w+0.62198)*Ta) ); Ca=((1.006*((Pa-w*Pa)/Pa))+(w/(1+w))*(1.8723))*1000; mwev=mweu/Pa; Pr=Ca*mweu/ka; Re=Pa*v*lxx/mweu; %Reynold's number Nu=0.0296*(Re^0.8)*Pr^(1/3); if Ta<Tc hcca=Nu*ka/lxx; else Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 63 hcca=-Nu*ka/lxx; end Vwh=vw*(log10((66.7*(0.872+0.149*lxx/3.05))-5.3))/2.11; %wind speed at the current height, m/s hcam=2.8+3.0*Vwh ; %cover heat loss coefficent to ambient air Rabed=(lxx^3)*g*raconstant*(Tb-Ta)*Pr/(Ta*mwev^2); Nubed=0.54*(Rabed^0.25); hcba=Nubed*ka/lxx; hrcs=emitcov*(sigma*(Tc^2 +TT)*(Tc+Tsk)); hrbc=sigma*(Tc+Tb)*(Tc^2+Tb^2)/(1/emitcov+1/emitbed-1); %heat transfer coefficient for radiation between cover and the drying bed %___________(density massflow rate x specific heat)___ Ga=Pa*v*Ca*Hd; Tbold=Tb; Tcold=Tc; Taold=Ta; Tb=(Rad2+Ta*hcba+Py+Tc*hrbc)/(hcba+hrbc+Tr); Tc=(Rad1+Tsk*hrcs+Tam*hcam+(Ab/Ac)*hrbc*Tb+Ta*hcca)/(hcam+hcca+hrcs+(Ab/Ac)*hrbc); Ta=Ta+(dx/Ga)*(hcca*(Tc-Ta) +hcba*(Tb-Ta)*(Ab/Ac)); CO=(-27405.526+97.5413*Ta-0.146244*Ta^2+0.12558*(10^-3)*Ta^3-0.48502*(10^-7)*Ta^4)/(4.34903*Ta-0.39381*10^(-2)*Ta^2 ); Pvs=22105649.25*exp(CO); %Saturated vapour pressure, Pa Pv=rh*Pvs; %vapour pressure of air in the heating chamber w=0.6219*Pv/(Patm-Pv); %Humidity ratio of air in the heating chamber, rh=Pv/Pvs; Vs=(287.07*Ta*(1+1.608*w))/Patm; h=1006.9254*(Ta-273.16)+w*(2512131.0+1552.4*(Ta-273.16)); qair=(Pa*dx*Ahc*(Ta-Ti)*Ca)+qair; % hcb1(k+1)=hcba;hcamm(k+1)=hcam;hc1(k+1)=hcca; Pvv(k+1)=Pv; Pvvs(k+1)=Pvs; px(T,k+1)=Pa;ha(T,k+1)=h; Tcc(T,k+1)=Tc; Tbb(T,k+1)=Tb; Taa(T,k+1)=Ta; wh(T,k+1)=w;rhr(T,k+1)=rh; Vss(T,k+1)=Vs; end Ehc=Ehc+(dt*Ach*E*Cons); Qairt=Qairt+(qair*v*dt/dx); nhc=(qair*v/dx)/(Ach*E*Cons);% nhc=qair/(dt*Ach*E); Nhc(T)=nhc; drytimes=drytimes+dt; %current total drying time, s drytimeh=drytimes/3600; %current total drying time, hrs %_________DRYING_PINEAPPLE_IN_ONE_MESH____ Rad22p=E*Cons*(trscov*abspdt)/(1-(1-abspdt)*refpdt); Hd=0.23; for meshes=1 % only one drying mesh was loaded that day %5CM WOODEN DISTANCE OF THE DRYING MESH, assuming conditions to vary slightly Mwlm=0; for wd=1:50/dxm k=k+1; lxx=lxx+dx; px(T,k+1)=Pa;ha(T,k+1)=h; Tcc(T,k+1)=Tc; Tbb(T,k+1)=Tb; Taa(T,k+1)=Ta; wh(T,k+1)=w;rhr(T,k+1)=rh; Vss(T,k+1)=Vs; end % ending the value transfer loop for dry=1:nc % looping for each of the five rows loaded that day lx=0; Mwl=0; Tpw=0; Ppw=0; Cpw=0; Qevt=0;%Tp, Pp, Cp weights of each pineapple slice node; mdb=mpd(T,dry); Mi=M(T,dry); Tp=Tppd(T,dry);%current mc db, mass, Kg and Tp, K mwb=mdb/(1+mdb); Tref=Tp;mdbref=mdb; mwbref=mwb; %current mc, wet basis for q=1:(b-1) %__________pineapple density and specfic heat____ mdbold=mdb; mwbold=mwb; Tpold=Tp; Pw=997.18-0.0031439*(Tp-273.16)-0.0037574*(Tp-273.16)^2; %pineapple water density, Kg/m^3 Pc=1599.19-0.31046*(Tp-273.16); %current pineapple carbohydrate density, Kg/m^3 Ppr=1329.9-0.5184*(Tp-273.16); %current pineapple Protein density, Kg/m^3 Pas=2423.8-0.28063*(Tp-273.16); %current pineapple ash density, Kg/m^3 Pf=925.59-0.41757*(Tp-273.16); %current pineapple fat density, Kg/m^3 Cw=4.1762-9.0864*(10^-5)*(Tp-273.16)+5.4731*(10^-6)*(Tp-273.16)^2; %current pineapple water shc, KJ/KgK Cpr=1.9842+1.4733*(10^-3)*(Tp-273.16)-4.8008*(10^-6)*(Tp-273.16)^2;%current pineapple protein shc, KJ/KgK Cc=1.54884+1.9625*(10^-3)*(Tp-273.16)-5.9399*(10^-6)*(Tp-273.16)^2; %current pineapple carbohydrate shc, KJ/KgK Cas=1.0926+1.8896*(10^-3)*(Tp-273.16)-3.6817*(10^-6)*(Tp-273.16)^2; %current pineapple ash shc, KJ/KgK Cf=1.9842+1.4733*(10^-3)*(Tp-273.16)-4.8008*(10^-6)*(Tp-273.16)^2; %current pineapple fat shc, KJ/KgK Pp=1/((mwb/Pw)+(((12.63/Pc)+(0.54/Ppr)+(0.22/Pas)+(0.12/Pf))/(13.51+(mwb*100)))); %current pineapple density, Kg/m^3 Cp=(mwb*Cw+(12.63*Cc+0.54*Cpr+0.22*Cas+0.12*Cf)/(13.51+(mwb*100)))*1000; %current pineapple specific heat, J/KgK %____________strip/nodal area, m^2 lx=lx+dx; lp=2*(r^2-(r-lx)^2)^0.5; %current width of pineapple strip, m Ap=nr*lp*dx; % Surface area of pineapple strip under consideration, m^2. Rad21p=abscov*(1+(Ap*trscov*refpdt/Ac))*E*Cons; %____________AIR PROPERTIES____________ lxx=lxx+dx; lcc=(lxx*lb/(2*(lb+lxx))); Pa=(Patm*(1+w)/(461.56*(w+0.62198)*Ta) ); Ca=((1.006*((Pa-w*Pa)/Pa))+(w/(1+w))*(1.8723))*1000; % __________EMC, k ,n and Lp____________ me=((14.431-0.07886*(Tp-273.16))/((1/rh) - 1)^(1/3.137) )/100; % equlbrium mc db% %K values for v=0.02 to 2m/s and Ta from from 30 to 55 celcius. if v>0.1 && Ta>(35+273.16) Kd=0.082; elseif v>=0.1 && Ta>(35+273.16) Kd=0.081; elseif v>=0.1 && Ta<(35+273.16) Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 64 Kd=0.077; elseif v<0.1 && Ta<(40+273.16) Kd=0.057; elseif v<0.1 && Ta>(40+273.16) Kd=0.06; end % np=0.13365+(1.9265*rh)-1.77431*(rh^2)+(0.009468*(Tp-273.16)); %exponent of time used in page equation Lp=2502535.259-2385.76424*(Tp-273.16);%Latent heat of vaporisation, J/Kg mdb=mdb+dtd*(mdbold-me)*-Kd; dmdb=mdb-mdbold; %change in mc, db mwb=mdb/(1+mdb); %new mc, wb dmwb=mwb-mwbref; %change in mc, wb Mw=nr*Mi*Ap*-dmwb/(Aptr*(1-mwbold)); rh=rh-(dx*Pp*dmwb)*(Ap/Ac)/(Pa*v*dt); % new RH Re=Pa*v*lxx/mweu; %Reynold's number %________HEAT TRANSFER COEFFICIENTS__________________________ hrcs=emitcov*(sigma*(Tc^2 +TT)*(Tc+Tsk)); hrpc=sigma*(Tc+Tp)*(Tc^2+Tp^2)/(1/emitcov+1/emitpdt-1); if Tp>Tc hrpc=-hrpc; end Rabed=(lxx^3)*g*raconstant*(Tb-Ta)*Pr/(Ta*mwev^2); Nubed=0.54*(Rabed^0.25); hcba=Nubed*ka/lxx; Pr=Ca*mweu/ka; mwev=mweu/Pa; %Prandtl's number & kinematic viscosity Nu=0.0296*(Re^0.8)*Pr^(1/3); if Ta<Tc hcca=Nu*ka/lxx; else hcca=-Nu*ka/lxx; end Vwh=vw*(log10((66.7*(1.021+0.095*(lxx-3.1)/5.01))-5.3))/2.11; %wind speed at the current height, m/s hcam=2.8+3.0*Vwh ; if Ta>Tp Rapine=(lcc^3)*g*raconstant*(Ta-Tp)*Pr/(Ta*mwev^2); Nupine=0.27*(Rapine^0.25); hcpa=Nupine*ka/lcc; else Rapine=(lcc^3)*g*raconstant*(Tp-Ta)*Pr/(Ta*mwev^2); Nupine=0.54*(Rapine^0.25); hcpa=-Nupine*ka/lcc; end %___________(density massflow rate x specific heat)___ Ga=Pa*v*Ca*Hd; Tbold=Tb; Tcold=Tc; Taold=Ta; Ta=Ta+(dx/Ga)*(hcca*(Tc-Ta) +(hcpa*(Tp-Ta)*Ap/Ac)); Tp=Tp+(dt*(Ap/Ac)*((-hrpc-hcpa)*Tp+Rad22p+hcpa*Ta+hrpc*Tc)/(Pp*zp*Cp))+(Ap/Ac)*((Cwv-1000*Cw)*Mw+Lp*Mw)/(Cp*nr*Mi); % new pineapple temperature % The Bed and cover temperatures reduce slightly are assumed constant Tpw=Tpw+(Tp*Ap/Aptr); Ppw=Ppw+(Pp*Ap/Aptr); Cpw=Cpw+(Cp*Ap/Aptr); Mwl=Mwl+Mw; % current mass lost of pineapple %________HUMIDITY RATIO CO=(-27405.526+97.5413*Ta-0.146244*Ta^2+0.12558*10^(-3)*Ta^3-0.48502*T^4)/(4.34903*Ta-0.39381*10^(-2)*Ta^2 ); Pvs=22105649.25*exp(CO); %Saturated vapour pressure, Pa Pv=rh*Pvs; w=0.6219*Pv/(Patm-Pv); Qevt=Qevt+(Mw*Lp+(nr*Mi*Ap*Cp*(Tp-Tref)/Aptr)); k=k+1; px(T,k+1)=Pa;ha(T,k+1)=h; Tcc(T,k+1)=Tc; Tbb(T,k+1)=Tb; Taa(T,k+1)=Ta; wh(T,k+1)=w;rhr(T,k+1)=rh; Vss(T,k+1)=Vs; Tp=Tref; mdb=mdbref; end Mwlt=Mwlt+Mwl; Mwlm=Mwlm+Mwl; mwbnew=((nr*Mi*mwbold)-Mwl)/(nr*Mi-Mwl); mdbnew=mwbnew/(1-mwbnew); Mnew=Mi-Mwl/nr; % drying chmber efficiency Ndcj=Qevt/((qair*v*dt/dx)+(meshes*1.2*nc*0.14*E*dt)); % effieciency of the entire dryer Nall=Qevt/((meshes*1.2*nc*0.14*E*Cons*dt)+Ach*E*Cons*dt); Ndc(T)=Ndcj; Nsd(T)=Nall; Qevtt=Qevtt+Qevt; Edc=Edc+(meshes*1.2*nc*0.14*E*Cons*dt); Etot=(dt*Ach*E*Cons)+(meshes*1.2*nc*0.14*E*Cons*dt)+Etot; dr=1000*Mwl/dtd; %current drying rate, g/hr Tppd(T+1,dry)=Tpw; Pppd(T+1,dry)=Ppw; Cppd(T+1,dry)=Cpw; mpd(T+1,dry)=mdbnew;mpdwb(T+1,dry)=mwbnew; M(T+1,dry)=Mnew; DR(T+1,dry)=dr; for tu=1:40/dxm %distance between pineapple slice rows k=k+1;lxx=lxx+dx; px(T,k+1)=Pa;ha(T,k+1)=h; Tcc(T,k+1)=Tc; Tbb(T,k+1)=Tb; Taa(T,k+1)=Ta; wh(T,k+1)=w;rhr(T,k+1)=rh; Vss(T,k+1)=Vs; Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 65 end end DRall=1000*Mwlm/dtd; Dra(T+1)=DRall;dra(T+1)=(DR(T+1,1)+DR(T+1,2)+DR(T+1,3)+DR(T+1,4)+DR(T+1,5)); for tt=1:100/dxm % distance between the last pineapple slice and the wood. k=k+1;lxx=lxx+dx; px(T,k+1)=Pa;ha(T,k+1)=h; Tcc(T,k+1)=Tc; Tbb(T,k+1)=Tb; Taa(T,k+1)=Ta; wh(T,k+1)=w;rhr(T,k+1)=rh; Vss(T,k+1)=Vs; end %5CM WOODEN DISTANCE OF THE DRYING MESH after drying, assuming conditions to vary slightly for wd2=1:50/dxm k=k+1;lxx=lxx+dx; px(T,k+1)=Pa;ha(T,k+1)=h; Tcc(T,k+1)=Tc; Tbb(T,k+1)=Tb; Taa(T,k+1)=Ta; wh(T,k+1)=w;rhr(T,k+1)=rh; Vss(T,k+1)=Vs; end % ending the value transfer loop for gx=80/dxm %distance between trays, air get's heated k=k+1;lxx=lxx+dx; lcc=(lxx*lb/(2*(lb+lxx))); Pa=(Patm*(1+w)/(461.56*(w+0.62198)*Ta) ); Ca=((1.006*((Pa-w*Pa)/Pa))+(w/(1+w))*(1.8723))*1000; mwev=mweu/Pa; Pr=Ca*mweu/ka; Re=Pa*v*lxx/mweu; %Reynold's number Nu=0.0296*(Re^0.8)*Pr^(1/3); if Ta<Tc hcca=Nu*ka/lxx; else hcca=-Nu*ka/lxx; end % ra=g*(Tc-Tam)*raconstant*(lcc^3)*Pr/(Tam*mwev^2);nusseltc=0.54*ra^0.25; hcam=nusseltc*ka/lcc; Rabed=(lxx^3)*g*raconstant*(Tb-Ta)*Pr/(Ta*mwev^2); Nubed=0.54*(Rabed^0.25); hcba=Nubed*ka/lxx; hrcs=emitcov*(sigma*(Tc^2 +TT)*(Tc+Tsk)); hrbc=sigma*(Tc+Tb)*(Tc^2+Tb^2)/(1/emitcov+1/emitbedburn-1); %heat transfer coefficient for radiation between cover and the drying bed %calculation of air temperature first, since it's a linear equation; Ta(i+1)=Ta(i)+dTa; %___________(density massflow rate x specific heat)___ Ga=Pa*v*Ca*Hd; Tbold=Tb; Tcold=Tc; Taold=Ta; Tb=(Rad2+Ta*hcba+Py+Tc*hrbc)/(hcba+hrbc+Tr); Tc=(Rad1+Tsk*hrcs+Tam*hcam+(Ab/Ac)*hrbc*Tb+Ta*hcca)/(hcam+hcca+hrcs+(Ab/Ac)*hrbc); Ta=Ta+(dx/Ga)*(hcca*(Tc-Ta) +hcba*(Tb-Ta)*(Ab/Ac)); CO=(-27405.526+97.5413*Ta-0.146244*Ta^2+0.12558*(10^-3)*Ta^3-0.48502*(10^-7)*Ta^4)/(4.34903*Ta-0.39381*10^(-2)*Ta^2 ); Pvs=22105649.25*exp(CO); %Saturated vapour pressure, Pa Pv=rh*Pvs; %vapour pressure of air in the heating chamber w=0.6219*Pv/(Patm-Pv); %Humidity ratio of air in the heating chamber, rh=Pv/Pvs; Vs=(287.07*Ta*(1+1.608*w))/Patm; h=1006.9254*(Ta-273.16)+w*(2512131.0+1552.4*(Ta-273.16)); px(T,k+1)=Pa;ha(T,k+1)=h; Tcc(T,k+1)=Tc; Tbb(T,k+1)=Tb; Taa(T,k+1)=Ta; wh(T,k+1)=w;rhr(T,k+1)=rh; Vss(T,k+1)=Vs; end end %____________END_PINEAPPLE_DRYING______ p=length(dx:dx:0.98); Radh1=abscov*E*(1+(Ab*trscov*refbedburn/Ac))*Cons; Radh2=E*Cons*(trscov*absbedburn)/(1-(1-absbedburn)*refbedburn); Hd=H-(Hh/2)+(W/4)*sin(angc)+0.01+0.02; for z=1:p k=k+1; lxx=lxx+dx; lcc=(lxx*lb/(2*(lb+lxx))); Ca=((1.006*((Pa-w*Pa)/Pa))+(w/(1+w))*(1.8723))*1000; Pa=(Patm*(1+w)/(461.56*(w+0.62198)*Ta) ); mwev=mweu/Pa; Pr=Ca*mweu/ka; Re=Pa*v*lxx/mweu; %Reynold's number Nu=0.0296*(Re^0.8)*Pr^(1/3); if Ta<Tc hcca=Nu*ka/lxx; else hcca=-Nu*ka/lxx; end Vwh=vw*(log10((66.7*(1.021+0.095*(lxx-4.03)/5.01))-5.3))/2.11; %wind speed at the current height, m/s hcam=2.8+3.0*Vwh ; Rabed=(lxx^3)*g*(Tb-Ta)*raconstant*Pr/(Ta*mwev^2); Nubed=0.54*(Rabed^0.25); hcba=Nubed*ka/lxx; hrcs=emitcov*(sigma*(Tc^2 +TT)*(Tc+Tsk)); hrbc=sigma*(Tc+Tb)*(Tc^2+Tb^2)/(1/emitcov+1/emitbed-1); %heat transfer coefficient for radiation between cover and the drying bed %calculation of air temperature first, since it's a linear equation; Ta(i+1)=Ta(i)+dTa; Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 66 %___________(density massflow rate x specific heat)___ Ga=Pa*v*Ca*Hd; Tbold=Tb; Tcold=Tc; Taold=Ta; Tb=(Radh2+Ta*hcba+Py+Tc*hrbc)/(hcba+hrbc+Tr); Tc=(Radh1+Tsk*hrcs+Tam*hcam+(Ab/Ac)*hrbc*Tb+Ta*hcca)/(hcam+hcca+hrcs+(Ab/Ac)*hrbc); Ta=Ta+(dx/Ga)*(hcca*(Tc-Ta) +hcba*(Tb-Ta)*(Ab/Ac)); CO=(-27405.526+97.5413*Ta-0.146244*Ta^2+0.12558*(10^-3)*Ta^3-0.48502*(10^-7)*Ta^4)/(4.34903*Ta-0.39381*10^(-2)*Ta^2 ); Pvs=22105649.25*exp(CO); %Saturated vapour pressure, Pa Pv=rh*Pvs; %vapour pressure of air in the heating chamber w=0.6219*Pv/(Patm-Pv); %Humidity ratio of air in the heating chamber, rh=Pv/Pvs; Vs=(287.07*Ta*(1+1.608*w))/Patm; h=1006.9254*(Ta-273.16)+w*(2512131.0+1552.4*(Ta-273.16)); % hcb1(k+1)=hcba;hcamm(k+1)=hcam;hc1(k+1)=hcca; Pvv(k+1)=Pv; Pvvs(k+1)=Pvs; px(T,k+1)=Pa;ha(T,k+1)=h; Tcc(T,k+1)=Tc; Tbb(T,k+1)=Tb; Taa(T,k+1)=Ta; wh(T,k+1)=w;rhr(T,k+1)=rh; Vss(T,k+1)=Vs; end gt=length(dx:dx:1.03); Rad11=abscov*E*(1+(Ab*trscov*refbedburn/Ac)); Rad22=E*(trscov*absbedburn)/(1-(1-absbedburn)*refbedburn); Vwh=vw*(log10((66.7*1.021)-5.3))/2.11; %wind speed at the current height, m/s hcam=2.8+3.0*Vwh ; for y=1:gt k=k+1; lxx=lxx+dx; lcc=(lxx*lb/(2*(lb+lxx))); Ca=((1.006*((Pa-w*Pa)/Pa))+(w/(1+w))*(1.8723))*1000; Pa=(Patm*(1+w)/(461.56*(w+0.62198)*Ta) ); mwev=mweu/Pa; Pr=Ca*mweu/ka; Re=Pa*v*lxx/mweu; %Reynold's number Nu=0.0296*(Re^0.8)*Pr^(1/3); if Ta<Tc hcca=Nu*ka/lxx; else hcca=-Nu*ka/lxx; end Rabed=(lxx^3)*g*(Tb-Ta)*Pr/(Ta*mwev^2); Nubed=0.54*(Rabed^0.25); hcba=Nubed*ka/lxx; hrcs=emitcov*(sigma*(Tc^2 +TT)*(Tc+Tsk)); hrbc=sigma*(Tc+Tb)*(Tc^2+Tb^2)/(1/emitcov+1/emitbed-1); %heat transfer coefficient for radiation between cover and the drying bed %calculation of air temperature first, since it's a linear equation; Ta(i+1)=Ta(i)+dTa; %___________(density massflow rate x specific heat)___ Ga=Pa*v*Ca*Hd; Tbold=Tb; Tcold=Tc; Taold=Ta; Tb=(Rad22+Ta*hcba+Py+Tc*hrbc)/(hcba+hrbc+Tr); Tc=(Rad11+Tsk*hrcs+Tam*hcam+(Ab/Ac)*hrbc*Tb+Ta*hcca)/(hcam+hcca+hrcs+(Ab/Ac)*hrbc); Ta=Ta+(dx/Ga)*(hcca*(Tc-Ta) +hcba*(Tb-Ta)*(Ab/Ac)); CO=(-27405.526+97.5413*Ta-0.146244*Ta^2+0.12558*(10^-3)*Ta^3-0.48502*(10^-7)*Ta^4)/(4.34903*Ta-0.39381*10^(-2)*Ta^2 ); Pvs=22105649.25*exp(CO); %Saturated vapour pressure, Pa Pv=rh*Pvs; %vapour pressure of air in the heating chamber w=0.6219*Pv/(Patm-Pv); %Humidity ratio of air in the heating chamber, rh=Pv/Pvs; Vs=(287.07*Ta*(1+1.608*w))/Patm; h=1006.9254*(Ta-273.16)+w*(2512131.0+1552.4*(Ta-273.16)); % hcb1(k+1)=hcba;hcamm(k+1)=hcam;hc1(k+1)=hcca; Pvv(k+1)=Pv; Pvvs(k+1)=Pvs; px(T,k+1)=Pa;ha(T,k+1)=h; Tcc(T,k+1)=Tc; Tbb(T,k+1)=Tb; Taa(T,k+1)=Ta; wh(T,k+1)=w;rhr(T,k+1)=rh; Vss(T,k+1)=Vs; end pl=length(dx:dx:3.041); Rad111=abscov*E*Cons7*(1+(Ab*trscov*refbedburn/Ac)); Rad222=E*Cons7*(trscov*absbedburn)/(1-(1-absbedburn)*refbedburn); for f=1:pl k=k+1; lxx=lxx+dx; lcc=(lxx*lb/(2*(lb+lxx))); Ca=((1.006*((Pa-w*Pa)/Pa))+(w/(1+w))*(1.8723))*1000; Pa=(Patm*(1+w)/(461.56*(w+0.62198)*Ta) ); mwev=mweu/Pa; Pr=Ca*mweu/ka; Re=Pa*v*lxx/mweu; %Reynold's number Nu=0.0296*(Re^0.8)*Pr^(1/3); if Ta<Tc hcca=Nu*ka/lxx; else hcca=-Nu*ka/lxx; end Vwh=vw*(log10((66.7*(1.021+(0.4644*(9.08-lxx)/3.04))-5.3)))/2.11; %wind speed at the current height, m/s hcam=2.8+3.0*Vwh ; Rabed=(lxx^3)*g*Ct*(Tb-Ta)*Pr/(Ta*mwev^2); Nubed=0.54*(Rabed^0.25); Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 67 hcba=Nubed*ka/lxx; hrcs=emitcov*(sigma*(Tc^2 +TT)*(Tc+Tsk)); hrbc=sigma*(Tc+Tb)*(Tc^2+Tb^2)/(1/emitcov+1/emitbed-1); %heat transfer coefficient for radiation between cover and the drying bed %___________(density massflow rate x specific heat)___ Ga=Pa*v*Ca*Hd; Tbold=Tb; Tcold=Tc; Taold=Ta; Tb=(Rad222+Ta*hcba+Py+Tc*hrbc)/(hcba+hrbc+Tr); Tc=(Rad111+Tsk*hrcs+Tam*hcam+(Ab/Ac)*hrbc*Tb+Ta*hcca)/(hcam+hcca+hrcs+(Ab/Ac)*hrbc); Ta=Ta+(dx/Ga)*(hcca*(Tc-Ta) +hcba*(Tb-Ta)*(Ab/Ac)); CO=(-27405.526+97.5413*Ta-0.146244*Ta^2+0.12558*(10^-3)*Ta^3-0.48502*(10^-7)*Ta^4)/(4.34903*Ta-0.39381*10^(-2)*Ta^2 ); Pvs=22105649.25*exp(CO); %Saturated vapour pressure, Pa Pv=rh*Pvs; %vapour pressure of air in the heating chamber w=0.6219*Pv/(Patm-Pv); %Humidity ratio of air in the heating chamber, rh=Pv/Pvs; Vs=(287.07*Ta*(1+1.608*w))/Patm; h=1006.9254*(Ta-273.16)+w*(2512131.0+1552.4*(Ta-273.16)); % hcb1(k+1)=hcba;hcamm(k+1)=hcam;hc1(k+1)=hcca; Pvv(k+1)=Pv; Pvvs(k+1)=Pvs; px(T,k+1)=Pa;ha(T,k+1)=h; Tcc(T,k+1)=Tc; Tbb(T,k+1)=Tb; Taa(T,k+1)=Ta; wh(T,k+1)=w;rhr(T,k+1)=rh; Vss(T,k+1)=Vs; end end % EXPERIMENTAL RESULTS Mfanwb=[0.8528,0.85096,0.84843,0.84582,0.84243,0.83363,0.8238,0.809736,0.79443,0.78055,0.76923,0.75831,0.74810,0.73699,0.72485]; Mconwb=[0.8528,0.85158,0.85034,0.84907,0.84714,0.84031,0.83285,0.82292,0.81074,0.80017,0.79082,0.78321,0.77644,0.76923,0.76153]; Mfandb=[5.79348,5.70961,5.59778,5.48595,5.34617,5.01069,4.67521,4.25586,3.86446,3.55694,3.33329,3.13759,2.96985,2.80211,2.63437]; Mcondb=[5.79348,5.73757,5.68165,5.62574,5.54187,5.26230,4.98273,4.64725,4.28381,4.00425,3.78056,3.61286,3.47307,3.33329,3.19351]; Exptime=[0,10,20,30,40,60,80,110,140,170,200,230,260,290,320]; %______________________________________________________________________ Nheatingchamber=Qairt/Ehc; Ndryingchamber=Qevtt/(Qairt+Edc); Ntotal=Qevtt/Etot; Nahc=Nhc(1:T); Nadc=Ndc(1:T); Ndryer=Nsd(1:T); Tp1=Tppd(1:t,1);Tp3=Tppd(1:t,3); Tp5=Tppd(1:t,5); m1=mpd(1:t,1); m3=mpd(1:t,3); m5=mpd(1:t,5); Mass1=M(1:t,1);Mass3=M(1:t,3);Mass5=M(1:t,5); mwb1=mpdwb(1:t,1); mwb3=mpdwb(1:t,3); mwb5=mpdwb(1:t,5); hhtime=1:T; htime=hhtime*(dt/60);Dra=Dra(1:T);dra=dra(1:T); Tat=Taa(1:T,1:n+1); Tbt=Tbb(1:T,1:n+1); Tct=Tcc(1:T,1:n+1); rhrx=rhr(1:T,1:n+1); whx=wh(1:T,1:n+1); hax=ha(1:T,1:n+1); pxx=px(1:T,1:n+1); Vssx=Vss(1:T,1:n+1); Ta=Tat-273.16; Tb=Tbt-273.16; Tc=Tct-273.16; M(1,:)=Mi; Pppd(1,1)=Pppd(1,2); Cppd(1,1)=Cppd(1,2); Pp1=Pppd(1:T,1); Pp3=Pppd(1:T,3); Pp5=Pppd(1:T,5); Cp1=Cppd(1:T,1); Cp3=Cppd(1:T,3); Cp5=Cppd(1:T,5); x=0:dx:l; x2=dx:dx:l; Tamx=mean(Ta); Tbmx=mean(Tb); Tcmc=mean(Tc); px=mean(pxx); ha=mean(hax); wh=mean(whx); Vss=mean(Vssx); rhr=100*mean(rhrx); TaT=mean(Ta,2); TbT=mean(Tb,2); TcT=mean(Tc,2); RHT=100*mean(rhrx,2); Mass1=0.5*Mass1; Mass3=0.5*Mass3; Mass5=0.5*Mass5; %________Exporting results to excel____ Miexpwb=[mpdwb(1,1);mpdwb(600/dt,1);mpdwb(1200/dt,1);mpdwb(1800/dt,1);mpdwb(2400/dt,1);mpdwb(3600/dt,1);mpdwb(4800/dt,1);mpdwb (6600/dt,1);mpdwb(8400/dt,1);mpdwb(12000/dt,1);mpdwb(12000/dt,1):mpdwb(13800/dt,1);mpdwb(15600/dt,1);mpdwb(17400/dt,1);mpdwb(T,1)] ; Miexpdb=[mpd(1,1);mpd(600/dt,1);mpd(1200/dt,1);mpd(1800/dt,1);mpd(2400/dt,1);mpd(3600/dt,1);mpd(4800/dt,1);mpd(6600/dt,1);mpd(8400/dt, 1);mpd(10200/dt,1);mpd(12000/dt,1);mpd(13800/dt,1);mpd(15600/dt,1);mpd(17400/dt,1);mpd(T,1)]; Massrow1=[Mass1(1,1);Mass1(600/dt,1);Mass1(1200/dt,1);Mass1(1800/dt,1);Mass1(2400/dt,1);Mass1(3600/dt,1);Mass1(4800/dt,1);Mass1(6600/dt,1); Mass1(8400/dt,1);Mass1(10200/dt,1);Mass1(12000/dt,1);Mass1(13800/dt,1);Mass1(15600/dt,1);Mass1(17400/dt,1);Mass1(T,1)]; Exptime2=[0;10;20;30;40;60;80;110;140;170;200;230;260;290;320]; % xlswrite('G:\odfinalresults.xls',Exptime);xlswrite('G:\odfinalresults1.xls',Massrow1); % xlswrite('G:\odfinalresults2.xls',Miexpwb); xlswrite('G:\odfinalresults3.xls',Miexpdb); %___________PLOTTING GRAPHS______________ figure plot(htime,TaT,'r',htime,TbT,'b',htime,TcT,'g',htime,RHT,'y','LineWidth',1.5) legend('Air ','Iron sheet Bed Temperature','Cover','RH') title(['Average Temperature of Cover,bed,air and RH values for v=',num2str(v),'m/s with time'],'FontSize',14) ylabel(['Temperature values ',' ^0','C'],'FontSize',14) xlabel('Drying Time (min)') axis([0 (T+(T/10)) 0 100]) grid on; grid minor hold off figure hold on plot(x,Tamx,x,Tcmc,'r',x, Tbmx,'g',x,rhr,'k','LineWidth',1.5) legend('Air Temperature','Cover Temperature','Drying bed','RH') axis([0 (l+.5) 0 100]) grid on;grid minor title(['Average point Temperature of Cover,bed,air and RH values for v=',num2str(v),'m/s'],'FontSize',14) ylabel(['Temperature values ',' ^0','C'],'FontSize',14) xlabel('Length of the dryer (m)') hold off Pp1(1)=Pp1(2);Pp3(1)=Pp3(2);Pp5(1)=Pp5(2); Cp1(1)=Cp1(2); Cp3(1)=Cp3(2); Cp5(1)=Cp5(2); Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 68 figure plot(htime,Pp1,htime,Cp1,'LineWidth',1.5 ) legend('Row1 Density','Row1 shc') title(['Simulated Pineapple Density and shc with time for v=',num2str(v),'m/s'],'FontSize',14) ylabel(['shc ','J/Kg ^0','C and Density Kg/m^3'],'FontSize',14); xlabel('Drying time (min)'); grid on;grid minor figure plot(htime,Nahc,htime,Nadc,htime,Ndryer) figure; plot(htime,m1,htime,m3, htime,m5,Exptime,Mfandb,Exptime,Mcondb,'LineWidth',1.5) title(['Drying curve for v=',num2str(v),'m/s'],'FontSize',14) ylabel('Moisture content %db','FontSize',14); xlabel('Drying time (min)'); legend('Row1','Row3','Row 5','Fansystem','Natural Convection') grid on;grid minor Tp1=Tp1-273.16; Tp3=Tp3-273.16; Tp5=Tp5-273.16; figure hold on plot(htime,Tp1,htime,Tp3,htime,Tp5,'LineWidth',1.5) title(['Simulated Pineapple temperature with time for v=',num2str(v),'m/s'],'FontSize',14) ylabel(['Temperature values ',' ^0','C'],'FontSize',14); xlabel('Drying time (min)'); legend('Row1','Row3','Row 5') grid on;grid minor hold off figure plot(htime,mwb1,htime,mwb3,htime,mwb5,Exptime,Mfanwb,Exptime,Mconwb,'LineWidth',1.5) title(['Drying curve for v=',num2str(v),'m/s'],'FontSize',14) ylabel('Moisture content %wb','FontSize',14); xlabel('Drying time (min)'); legend('Row1','Row3','Row 5','Fansystem','Natural Convection') grid on;grid minor figure plot(htime, Mass1, htime, Mass3, htime, Mass5) title(['Simulated Average Half Pineapple Slice Mass with time for v=',num2str(v),'m/s'],'FontSize',14) ylabel('Mass, Kg ','FontSize',14); xlabel('Drying time (min)') ;legend('Row1','Row3','Row 5'); grid on;grid minor figure DR1=sum(DR,2); DR1=DR1(2:T+1); plot(htime,DR1) title(['Instantaneous Drying rate of one mesh with time for v=',num2str(v),'m/s (80 slices)'],'FontSize',14) ylabel('Drying rate, g/hr ','FontSize',14); xlabel('Drying time (min)') ; tend=clock; gt2=toc; tcpuend=cputime;time= tcpuend-tcpu; %gt2 is the time the script required to run APPENDIX 2: Script to estimate drying air temperature, density, humidity ratio, enthalpy, RH, specific volume and shc along the dryer’s length. %GULU UNIVERSITY; SOLAR DRYER HEATING MODEL %By OBIRA DANIEL 4th year Biosystems Engineering project, %SUPERVISED BY ENG.BEN EBANGU ORARI AND PROF. YUN SOL CHOL clear tstart=clock; tcpu=cputime; tic; ticID=tic; tick=ticID; %parameters to estimate required processor time dx=1/1000; %______________________Physical constants declaration_______________________ sigma=5.667e-8; g=9.81; R=287.07; %___________________physical properties of the dryer collector/input values____________________________ angd=(2.8*pi/180); angc=(4.8*pi/180); W=1.22; zin=0.02;H=0.24; Hh=0.02;angb=(28*pi/180); E=750; %______________________ Calculated dimensional properties of the dryer's collector________________________ h=H-Hh;w=W-2*zin; %height form the top of v-groove/corrugated surface to the horizontal base of the cover support lc=W/cos(angc);Adh=(Hh*w/2)+h*w+(((tan(angc))*w^2)/4);%transvere cross-sectional length of collector, m lb=w/cos(angb); %transvere cross-sectional length of drying bed, m Hdb=4*Adh/(lb+(2*h)+lc); %Hydraulic diameter of the drying chamber, m Hd=H-(Hh/2)+(W/4)*sin(angc)+0.01; %average distance between cover and drying bed, m %_________________corrugated drying bed properties_________ refbed=0.1;absbed=0.8;emitbed=0.9;anglebd=2*(90-angb);kpy=0.029;zpy=7/1000; absbedburn=0.75;refbedburn=0.25;emitbedburn=0.23; %_________________cover physical properties_________ abscov=0.08;trscov=0.8;emitcov=0.8; %__________initial and boundary conditions, Temperature converted to kelvin scale_________ Tam=28+273.16;Ta=28+273.16;Tc=29+273.16;Tb=45+273.16;Tsk=0.0552*Tam^1.5;v=0.056; %____________Calcalation of any constant terms_________________________________ Ac=lc*dx;Ab=lb*dx; TT=Tsk^2; Rad1=abscov*E*(1+(Ab*trscov*refbed/Ac)*cos(angd)*cos(angc)); Rad2=((trscov*absbed)/(1-((1-absbed)*refbed)))*E*cos(angd)*cos(angc); %___________________________initialising a ones results matrix for each l=9.08;n=length(dx:dx:l);hc1=ones(1,(n+1)); Pvv=ones(1,(n+1));Pvvs=ones(1,(n+1)); Tcc=ones(1,(n+1)); Tbb=ones(1,(n+1)); Taa=ones(1,(n+1)); hcb1=ones(1,(n+1)); Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 69 Tcc(1)=Tc; Tbb(1)=Tb; Taa(1)=Ta;rhr=ones(1,(n+1));wh=ones(1,(n+1));hcamm=ones(1,n+1); %____________________________constant terms used in the looping____________ Tr=kpy/zpy;rh=0.61445;rhr(1)=rh;Vss=ones(1,(n+1));kx=length(dx:dx:3.05);ha=ones(1,n+1); Py=Tam*Tr; lxx=0;ka=0.026;mweu=1.85e-5; w=0.0166;px=ones(1,n+1); vw=1.5; % h1=linspace(0.872,1.021,1000*l/dxm); h2=linspace(1.021,1.116,1960/dxm); h4=linspace(1.116,1.4854,3040/dxm); for k=1:kx %calculation of air properties since they vary with temperature; lxx=lxx+dx; lcc=(lxx*lb/(2*(lb+lxx))); Pa=(89200*(1+w)/(461.56*(w+0.62198)*Ta) ); Ca=((1.006*((Pa-w*Pa)/Pa))+(w/(1+w))*(1.8723))*1000; mwev=mweu/Pa; Pr=Ca*mweu/ka; Re=Pa*v*lxx/mweu; %Reynold's number Nu=0.0296*(Re^0.8)*Pr^(1/3); if Ta<Tc hcca=Nu*ka/lxx; else hcca=-Nu*ka/lxx; end % ra=g*(Tc-Tam)*cos(angd)*(lxx^3)*Pr/(Tam*mwev^2); % nusseltc=0.54*ra^0.25; % hcam=nusseltc*ka/lcc; Vwh=vw*(log10((66.7*(0.872+0.149*lxx/3.05))-5.3))/2.11; %wind speed at the current height, m/s hcam=2.8+3.0*Vwh ; Rabed=(lxx^3)*g*cos(angd)*(Tb-Ta)*Pr/(Ta*mwev^2); Nubed=0.54*(Rabed^0.25); hcba=Nubed*ka/lxx; hrcs=emitcov*(sigma*(Tc^2 +Tsk^2)*(Tc+Tsk)); hrbc=sigma*(Tc+Tb)*(Tc^2+Tb^2)/(1/emitcov+1/emitbed-1); %heat transfer coefficient for radiation between cover and the drying bed %calculation of air temperature first, since it's a linear equation; Ta(i+1)=Ta(i)+dTa; %___________(density massflow rate x specific heat)___ Ga=Pa*v*Ca*Hd; Tbold=Tb; Tcold=Tc; Taold=Ta; Tb=(Rad2+Ta*hcba+Py+Tc*hrbc)/(hcba+hrbc+Tr); Tc=(Rad1+Tsk*hrcs+Tam*hcam+(Ab/Ac)*hrbc*Tb+Ta*hcca)/(hcam+hcca+hrcs+(Ab/Ac)*hrbc); Ta=Ta+(dx/Ga)*(hcca*(Tc-Ta) +hcba*(Tb-Ta)*(Ab/Ac)); CO=(-27405.526+97.5413*Ta-0.146244*Ta^2+0.12558*(10^-3)*Ta^3-0.48502*(10^-7)*Ta^4)/(4.34903*Ta-0.39381*10^(-2)*Ta^2 ); Pvs=22105649.25*exp(CO); %Saturated vapour pressure, Pa Pv=rh*Pvs; %vapour pressure of air in the heating chamber w=0.6219*Pv/(89200-Pv); %Humidity ratio of air in the heating chamber, rh=Pv/Pvs; Vs=(287.07*Ta*(1+1.608*w))/89200; h=1006.9254*(Ta-273.16)+w*(2512131.0+1552.4*(Ta-273.16)); ha(k+1)=h; px(k+1)=Pa;hcamm(k+1)=hcam; Tcc(k+1)=Tc; Tbb(k+1)=Tb; Taa(k+1)=Ta; hc1(k+1)=hcca; hcb1(k+1)=hcba; wh(k+1)=w;rhr(k+1)=rh; Pvv(k+1)=Pv; Pvvs(k+1)=Pvs;Vss(k+1)=Vs; end p=length(dx:dx:1.96); Radh1=abscov*E*(1+(Ab*trscov*refbedburn/Ac)*cos(angd)*cos(angc)); Radh2=E*cos(angd)*cos(angc)*(trscov*absbedburn)/(1-((1-absbedburn)*refbedburn)); Hd=Hd+0.02; for t=1:p k=k+1; lxx=lxx+dx; lcc=(lxx*lb/(2*(lb+lxx))); Ca=((1.006*((Pa-w*Pa)/Pa))+(w/(1+w))*(1.8723))*1000; Pa=(89200*(1+w)/(461.56*(w+0.62198)*Ta) ); mwev=mweu/Pa; Pr=Ca*mweu/ka; Re=Pa*v*lxx/mweu; %Reynold's number if Ta<Tc hcca=Nu*ka/lxx; else hcca=-Nu*ka/lxx; end % ra=g*(Tc-Tam)*cos(angd)*(lcc^3)*Pr/(Tam*mwev^2); % nusseltc=0.54*ra^0.25; % hcam=nusseltc*ka/lcc; Vwh=vw*(log10((66.7*(1.021+0.095*(lxx-3.05)/5.01))-5.3))/2.11; %wind speed at the current height, m/s hcam=2.8+3.0*Vwh ; Rabed=(lxx^3)*g*(Tb-Ta)*cos(angd)*Pr/(Ta*mwev^2); Nubed=0.54*(Rabed^0.25); hcba=Nubed*ka/lxx; hrcs=emitcov*(sigma*(Tc^2 +Tsk^2)*(Tc+Tsk)); hrbc=sigma*(Tc+Tb)*(Tc^2+Tb^2)/(1/emitcov+1/emitbed-1); %heat transfer coefficient for radiation between cover and the drying bed %calculation of air temperature first, since it's a linear equation; Ta(i+1)=Ta(i)+dTa; %___________(density massflow rate x specific heat)___ Ga=Pa*v*Ca*Hd; Tbold=Tb; Tcold=Tc; Taold=Ta; Tb=(Radh2+Ta*hcba+Py+Tc*hrbc)/(hcba+hrbc+Tr); Tc=(Radh1+Tsk*hrcs+Tam*hcam+(Ab/Ac)*hrbc*Tb+Ta*hcca)/(hcam+hcca+hrcs+(Ab/Ac)*hrbc); Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 70 Ta=Ta+(dx/Ga)*(hcca*(Tc-Ta) +hcba*(Tb-Ta)*(Ab/Ac)); CO=(-27405.526+97.5413*Ta-0.146244*Ta^2+0.12558*(10^-3)*Ta^3-0.48502*(10^-7)*Ta^4)/(4.34903*Ta-0.39381*10^(-2)*Ta^2 ); Pvs=22105649.25*exp(CO); %Saturated vapour pressure, Pa Pv=rh*Pvs; %vapour pressure of air in the heating chamber w=0.6219*Pv/(89200-Pv); %Humidity ratio of air in the heating chamber, rh=Pv/Pvs; Vs=(287.07*Ta*(1+1.608*w))/89200; px(k)=Pa;hcamm(k)=hcam; h=1006.9254*(Ta-273.16)+w*(2512131.0+1552.4*(Ta-273.16)); ha(k)=h; Tcc(k)=Tc; Tbb(k)=Tb; Taa(k)=Ta; hc1(k)=hcca; hcb1(k)=hcba; wh(k)=w;rhr(k)=rh; Pvv(k)=Pv; Pvvs(k)=Pvs;Vss(k)=Vs; end gt=length(dx:dx:1.03); Rad11=abscov*E*(1+(Ab*trscov*refbedburn/Ac)); Rad22=E*(trscov*absbedburn)/(1-((1-absbedburn)*refbedburn)); Vwh=vw*(log10((66.7*1.021)-5.3))/2.11; %wind speed at the current height, m/s hcam=2.8+3.0*Vwh ; for y=1:gt k=k+1; lxx=lxx+dx; lcc=(lxx*lb/(2*(lb+lxx))); Ca=((1.006*((Pa-w*Pa)/Pa))+(w/(1+w))*(1.8723))*1000; Pa=(89200*(1+w)/(461.56*(w+0.62198)*Ta) ); mwev=mweu/Pa; Pr=Ca*mweu/ka; Re=Pa*v*lxx/mweu; %Reynold's number if Ta<Tc hcca=Nu*ka/lxx; else hcca=-Nu*ka/lxx; end % ra=g*(Tc-Tam)*(lxx^3)*Pr/(Tam*mwev^2); % nusseltc=0.54*ra^0.25; % hcam=nusseltc*ka/lcc; Rabed=(lxx^3)*g*(Tb-Ta)*Pr/(Ta*mwev^2); Nubed=0.54*(Rabed^0.25); hcba=Nubed*ka/lxx; hrcs=emitcov*(sigma*(Tc^2 +Tsk^2)*(Tc+Tsk)); hrbc=sigma*(Tc+Tb)*(Tc^2+Tb^2)/(1/emitcov+1/emitbed-1); %heat transfer coefficient for radiation between cover and the drying bed %calculation of air temperature first, since it's a linear equation; Ta(i+1)=Ta(i)+dTa; %___________(density massflow rate x specific heat)___ Ga=Pa*v*Ca*Hd; Tbold=Tb; Tcold=Tc; Taold=Ta; Tb=(Rad22+Ta*hcba+Py+Tc*hrbc)/(hcba+hrbc+Tr); Tc=(Rad11+Tsk*hrcs+Tam*hcam+(Ab/Ac)*hrbc*Tb+Ta*hcca)/(hcam+hcca+hrcs+(Ab/Ac)*hrbc); Ta=Ta+(dx/Ga)*(hcca*(Tc-Ta) +hcba*(Tb-Ta)*(Ab/Ac)); CO=(-27405.526+97.5413*Ta-0.146244*Ta^2+0.12558*(10^-3)*Ta^3-0.48502*(10^-7)*Ta^4)/(4.34903*Ta-0.39381*10^(-2)*Ta^2 ); Pvs=22105649.25*exp(CO); %Saturated vapour pressure, Pa Pv=rh*Pvs; %vapour pressure of air in the heating chamber w=0.6219*Pv/(89200-Pv); %Humidity ratio of air in the heating chamber, rh=Pv/Pvs; Vs=(287.07*Ta*(1+1.608*w))/89200; h=1006.9254*(Ta-273.16)+w*(2512131.0+1552.4*(Ta-273.16)); ha(k)=h; px(k)=Pa;hcamm(k)=hcam; Tcc(k)=Tc; Tbb(k)=Tb; Taa(k)=Ta; hc1(k)=hcca; hcb1(k)=hcba; wh(k)=w;rhr(k)=rh; Pvv(k)=Pv; Pvvs(k)=Pvs;Vss(k)=Vs; end pl=length(dx:dx:3.041); Rad111=abscov*E*(1+(Ab*trscov*refbedburn/Ac)*cos(7*pi/180)*cos(4.9*pi/180)); Rad222=E*cos(7*pi/180)*cos(4.9*pi/180)*(trscov*absbedburn)/(1-((1-absbedburn)*refbedburn)); angl=7*pi/180;Ct=cos(7*pi/180); for f=1:pl k=k+1; lxx=lxx+dx; lcc=(lxx*lb/(2*(lb+lxx))); Ca=((1.006*((Pa-w*Pa)/Pa))+(w/(1+w))*(1.8723))*1000; Pa=(89200*(1+w)/(461.56*(w+0.62198)*Ta) ); mwev=mweu/Pa; Pr=Ca*mweu/ka; Re=Pa*v*lxx/mweu; %Reynold's number if Ta<Tc hcca=Nu*ka/lxx; else hcca=-Nu*ka/lxx; end % ra=g*(Tc-Tam)*(lxx^3)*Ct*Pr/(Tam*mwev^2); % nusseltc=0.54*ra^0.25; % hcam=nusseltc*ka/lcc; Vwh=vw*(log10((66.7*(1.021+(0.4644*(lxx-6.04)/3.04))-5.3)))/2.11; %wind speed at the current height, m/s hcam=2.8+3.0*Vwh ; Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 71 Rabed=(lxx^3)*g*Ct*(Tb-Ta)*Pr/(Ta*mwev^2); Nubed=0.54*(Rabed^0.25); hcba=Nubed*ka/lxx; hrcs=emitcov*(sigma*(Tc^2 +Tsk^2)*(Tc+Tsk)); hrbc=sigma*(Tc+Tb)*(Tc^2+Tb^2)/(1/emitcov+1/emitbed-1); %heat transfer coefficient for radiation between cover and the drying bed %calculation of air temperature first, since it's a linear equation; Ta(i+1)=Ta(i)+dTa; %___________(density massflow rate x specific heat)___ Ga=Pa*v*Ca*Hd; Tbold=Tb; Tcold=Tc; Taold=Ta; Tb=(Rad222+Ta*hcba+Py+Tc*hrbc)/(hcba+hrbc+Tr); Tc=(Rad111+Tsk*hrcs+Tam*hcam+(Ab/Ac)*hrbc*Tb+Ta*hcca)/(hcam+hcca+hrcs+(Ab/Ac)*hrbc); Ta=Ta+(dx/Ga)*(hcca*(Tc-Ta) +hcba*(Tb-Ta)*(Ab/Ac)); CO=(-27405.526+97.5413*Ta-0.146244*Ta^2+0.12558*(10^-3)*Ta^3-0.48502*(10^-7)*Ta^4)/(4.34903*Ta-0.39381*10^(-2)*Ta^2 ); Pvs=22105649.25*exp(CO); %Saturated vapour pressure, Pa Pv=rh*Pvs; %vapour pressure of air in the heating chamber w=0.6219*Pv/(89200-Pv); %Humidity ratio of air in the heating chamber, rh=Pv/Pvs; Vs=(287.07*Ta*(1+1.608*w))/89200; h=1006.9254*(Ta-273.16)+w*(2512131.0+1552.4*(Ta-273.16)); ha(k)=h; px(k)=Pa;hcamm(k)=hcam; Tcc(k)=Tc; Tbb(k)=Tb; Taa(k)=Ta; hc1(k)=hcca; hcb1(k)=hcba; wh(k)=w;rhr(k)=rh; Pvv(k)=Pv; Pvvs(k)=Pvs;Vss(k)=Vs; end Ta=Taa-273.16;Pvs(1)=22105649.25*exp(-27405.526+97.5413*Tam-0.146244*Tam^2+0.12558*(10^-3)*Tam^3-0.48502*(10^7)*Tam^4)/(4.34903*Tam-0.39381*10^(-2)*Tam^2 ); Tb=Tbb-273.16;wh(1)=wh(2);Pvv(1)=rh*Pvs(1); Tc=Tcc-273.16; rhr=100*rhr; x=0:dx:l;Vss(1)=(287.07*Tam*(1+1.608*wh(1)))/89200; x2=dx:dx:l; figure; plot(x,Ta,'LineWidth',1.5) hold on plot(x,Tc,'r','LineWidth',1.5) plot(x,Tb,'g','LineWidth',1.5) plot(x,rhr,'k','LineWidth',1.5) legend('Air Temperature','Cover Temperature','Drying bed','RH') axis([0 (l+.5) 0 100]) grid on grid minor ylabel(['Temperature values ',' ^0','C'],'FontSize',14) xlabel('Length of the drying chamber (m)') title(['Temperature distribution along the entire dryer with v=',num2str(v),'m/s and E=',num2str(E),'W/m^2'],'FontSize',14) figure plot(x,hcb1,x,hc1,x,hcamm,'LineWidth',1.5) ylabel('Heat transfer coefficients W/m^2') xlabel('Length of the drying chamber (m)') title(['Heat transfer coefficients along the entire dryer with v=',num2str(v),'m/s and E=',num2str(E),'W/m^2'],'FontSize',14) legend('hcba(air-bed)','hcca(air-cover)','hcam(cover-ambient air)') grid on; grid minor hold off figure plot(x,wh,x,Vss,x,px,'LineWidth',1.5) ylabel('Kg H_2O/Kg Dry air, m^3 H_20/Kg Dry air or Kg/m^3 ') xlabel('Length of the drying chamber (m)') title(['Humidity ratio, Specific Volume and Air Density along the entire dryer with v=',num2str(v),'m/s and E=',num2str(E),'W/m^2'],'FontSize',14) legend('Humidity Ratio ','Specific Volume','Air Density') axis([0 (l+1) 0 (Vss(n)+0.3)]) grid on; grid minor hold off figure ha(1)=1006.9254*(Tam-273.16)+wh(1)*(2512131.0+1552.4*(Tam-273.16)); hakg=(1/1000)*ha; plot(x,hakg,'LineWidth',1.5) ylabel('KJ/Kg ','FontSize',14) xlabel('Length of the drying chamber (m)') title(['Air Enthalpy along the entire dryer with v=',num2str(v),'m/s and E=',num2str(E),'W/m^2'],'FontSize',14) grid on; grid minor axis([-0.5 (l+.5) 70 680]) tend=clock; gt2=toc; tcpuend=cputime;time= tcpuend-tcpu; APPENDIX 3: Making MATLAB simulations faster using parallelization and GPGPU. Parallelization in computing is a technique of dividing a computational load to smaller parts; these smaller loads are all computed simultaneously. In MALAB, it is useful in Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 72 cases where the results are continuously decreasing or increasing like the air temperature in ad dryer. MATLAB uses a data parallelism technique to perform it’s parallelization. Unfortunately for a solar dryer simulation, the next values depend on the current values thus this makes it impossible to parallelize the script without getting wrong results. To parallelize in MATLAB, additional workers are loaded/added to a matlab pool (threads (smallest computer execution units) that matlab uses), thus the number of possible simultaneous executions increases. To use the newly created threads, the parfor (parallel for) loop is used instead of the for loop. It is very useful if you want to execute the same computations on all values of a given dataset faster not matter the sequence of execution. GPGPU is a computing technique that uses graphics processing units to perform computations normally done by a system microprocessor. Graphics cards have several cores and are more powerful than ordinary processors but have a limited data scope and instruction set or programmability. However due to their architecture they are very suitable for parallel loads or very intensive calculations. The computer used to write this report has a Pentium Dual Core E5700 @3.0Ghz and GeForce GT 440. The E5700 has an average peak performance of 24Gflops while the GT440 has a peak performance of 288Gflops. CUDA is a parallel computing architecture developed by NVidia for and used by their GPUs to perform GPGPU. MATLAB has inbuilt support for CUDA API and most of it’s mathematical functions can be calculated on GPUS, making it easy to perform GPU assisted calculations, it currently has no support for AMD cards. To perform GPU assisted calculations, a GPU is chosen using gpuDevice, then variables from the computer memory can be transferred to the GPU memory or directly created there using gpuarray. Any calculations are then carried out normally. An average Pentium Dual Core laptop of 2-2.3Ghz has a peak double precision floating point arithmetic performance of 16-18Gflops and an Intel graphics unit that cannot be used for GPGPU since it has no programming interface and architecture and is coupled with a number fewer of graphics processing cores. APPENDIX 4: Equations for most used MSI models. Gulu University Solar Dryer Computer Model, Biosystems Engineering Obira Daniel 2012 73 The following equations are used to predict me for most of agricultural crops especially cereals and grains during drying based on the RH and product temperature, T (0C). A, B and C are constants that depend on the crop variety, RH is in decimal format. 1. Modified Henderson equation; 2. Modified Chung-Pfost equation; 3. Modified Hasley equation; 4. Modified Oswin equation (used in this model); 5. Guggenheim-Anderson-deBoer (GAB) equation; The above equations are from (ASAE Standards D245.5, 1998) and the constants A, B and C used in the model can also be got from the same paper. APPENDIX 5: Relations for calculating Nusselt’s Number; 1. Natural Convection; Characteristic length, lc=Bed Surface Area/Perimeter; Heating flowing air from below or flowing air heating a surface above it; Heating flowing air from above or flowing air heating a surface below it (pineapple); Turbulent flow; 2. 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