ABSTRACT
In this work, a low dimensional lumped parameter model describing the variation of moisture content and temperature of the potato chips undergoing drying in a batch tray dryer is developed using conservation of mass and energy. The model also captures the temperature and moisture content dynamics of the air draft in the dryer. Experimental data obtained were obtained using a computer controlled batch tray drier equipped with automatic data logging facility in the Chemical Engineering Laboratory of Afe Babalola University, Ado-Ekiti, Ekiti State, Nigeria. The differential equations derived were solved with the aid of MATLAB using ode45 function. There was close agreement between experimental data and simulation result. The variation of the potato temperature and moisture content obtained from the model followed the trend observed in the experiment. This simple model can thus be used to configure an appropriate controller to regulate the drying temperature, moisture content as well as the air draft temperature.
vi
TABLE OF CONTENTS
CERTIFICATION ………………………………………………………………………………………………………………………. ii
DEDICATION …………………………………………………………………………………………………………………………… iii
ACKNOWLEDGEMENT …………………………………………………………………………………………………………… iv
ABSTRACT ……………………………………………………………………………………………………………………………….. v
LIST OF FIGURES ………………………………………………………………………………………………………………….. viii
NOMENCLATURE …………………………………………………………………………………………………………………… ix
CHAPTER ONE …………………………………………………………………………………………………………………………. 1
1.0 INTRODUCTION ………………………………………………………………………………………………………… 1
1.1 Background ……………………………………………………………………………………………………………….. 1
1.2 Statement of Problem ………………………………………………………………………………………………… 2
1.3 Scope of Study ………………………………………………………………………………………………………….. 3
1.4 Aim of Study ……………………………………………………………………………………………………………… 3
1.5 Objectives ………………………………………………………………………………………………………………….. 3
1.6 Justification ……………………………………………………………………………………………………………….. 4
CHAPTER TWO ………………………………………………………………………………………………………………………… 5
2.0 THEORETICAL BACKGROUND AND LITERATURE REVIEW ……………………………………… 5
2.1 Theoretical Background ……………………………………………………………………………………………… 5
2.2 LITERATURE REVIEW …………………………………………………………………………………………….. 26
CHAPTER THREE …………………………………………………………………………………………………………………… 35
3.0 METHODOLOGY …………………………………………………………………………………………………………… 35
3.1 Methodology Overview ……………………………………………………………………………………………. 35
3.2 Model Formulation ……………………………………………………………………………………………………. 35
3.4 Equipment and Experimental Procedure …………………………………………………………………………… 43
CHAPTER FOUR ……………………………………………………………………………………………………………………… 47
4.0 RESULT AND DISCUSSION …………………………………………………………………………………………… 47
4.2 Variation of Simulated and Experimental Air Temperature with Time ………………………………. 48
4.3 Variation of Moisture Content with Time ……………………………………………………………………….. 50
5.0 CONCLUSION AND RECCOMENDATION ……………………………………………………………………. 51
5.1 Conclusion …………………………………………………………………………………………………………………… 51
5.2 Recommendation ………………………………………………………………………………………………………….. 51
APPENDIX ………………………………………………………………………………………………………………………………. 54
vii
Appendix A …………………………………………………………………………………………………………………………… 54
Antoine Table………………………………………………………………………………………………………………………… 54
Appendix B …………………………………………………………………………………………………………………………… 54
Simulation codes ……………………………………………………………………………………………………………………. 54
Appendix C …………………………………………………………………………………………………………………………… 56
Experimental Data …………………………………………………………………………………………………………………. 56
viii
LIST OF FIGURES
Figure 2. 1 Rate of drying of a granular material ………………………………………………………………… 9
Figure 2. 2 The use of a rate of drying curve in estimating the time for drying ……………………… 11
Figure 2. 3: 2. 4 Rotary dryer, 0.75 m diameter × 4.5 m long for drying dessicated coconut ….. 15
Figure 2. 4: Flow diagram for a typical continuous fluidized-bed dryer ……………………………….. 18
Figure 2. 5Air-lift dryer with an integral mill ……………………………………………………………………. 21
Figure 2. 6: Turbo-shelf dryer …………………………………………………………………………………………. 22
Figure 3. 2: Air system in a tray drier ………………………………………………………………………………. 39
Figure 3. 3: Schematic diagram of a tray dryer …………………………………………………………………. 43
ix
NOMENCLATURE
SYMBOLS MEANING UNITS
Hsys Enthalpy of the system kJ
Hout Enthalpy kJ
WD Rate of drying
m s
kg
2
hw Enthalpy of water kJ/kg
Mw Mass of water of the system Kg
Ms Mass of solid kg
Qconvection Heat due to convection kJ
hv(water) Latent heat of vaporization kg/kJ
T Temperature of the potato K
Tref Reference temperature K
Cps Specific heat capacity of
potato
kg/kJ
Cpw Specific heat capacity of water kg/kJ
Cpv Specific heat capacity of vapor kg/kJ
WB Flow rate of air kg/s
CB Specific heat capacity of air kg/kJ
Tgo Inlet temperature of the air K
x
Tg Outlet temperature of the air K
Heat transfer coefficient
m K
kW
2
A Interfacial Area 2 m
Yo Humidity of inlet air kg/kg
Y Humidity of outlet air Kg/kg
H Humidity Kg/kg
%RH Percentage humidity No unit
Pw Partial pressure of water
N/
m2
Pwo Vapor pressure
N/
m2
P*
Vapor pressure
N/
m2
Nu Nusselt number No unit
Pr Prandtl number No unit
Re Reynolds number No unit
Sc Schmidt number No unit
P Total pressure
N /
m2
bulk
Pw
Partial pressure/vapor pressure
of component ms2
kg
surface
Pw
Partial pressure of water vapor
in the air at the solid interface ms2
kg
air
Pw
Partial vapor of water vapor in
air
ms2
kg
xi
Symbol
Meaning
Density
Units
m3
kg
air Density of air
m3
kg
k Mass transfer coefficient
s
m
kc Mass transfer for a convective
driving force
s
m
k p Mass transfer coefficient for a
partial pressure
m s
kg
2
L Length of drying Layer m
air Viscosity of air
m s
kg
.
Cpair Specific capacity of air kJ/kg
kair Thermal conductivity of air
mK
W
X Moisture content No unit
1
CHAPTER ONE
1.0 INTRODUCTION
1.1 Background
The drying process is a complex process of heat and mass transfer resulting in a direct transfer of humidity from some substance into hot air. The heat transfer, necessary for that process, can be direct, convective from the drying agent which flows around the drying material, or indirect, by different procedure (Salemović et al., 2014). Drying process has long been used from the time of old to dry food. For example, foods like meat, fish and so on were dried using sun as the drying medium to preserve them and prevent growth of micro –organisms (Dagbe et al., 2014). Majorly, substances are/were dried for the following reasons:
1. To remove moisture content which may otherwise lead to corrosion. One example is drying of gaseous fuels or benzene prior to chlorination.
2. To reduce the cost of transportation.
3. To make material more suitable for handling, as for soap powders, dye stuffs and fertilizers.
4. To provide definite properties, such as for example maintaining free flowing of salt.
5. To mitigate the activities of the micro-organisms that can cause spoilage and decay in food products if moisture were present in the food.
Modeling of drying processes and kinetics is a tool for process control and necessary to choose suitable method of drying for a specific product. Developed models fall into three categories namely the theoretical, semi-theoretical and empirical. Semi-theoretical models offer a compromise between theory and ease of application (Khazaei and Daneshmandi, 2007). Semi-
2
theoretical models are Lewis, Page, Henderson and Pabis, logarithmic, two terms and two terms exponential, models are used widely for designing as well as selection of optimum drying conditions and for accurate prediction of simultaneous heat and mass transfer phenomena during drying process. It also leads to the production of high quality product and increase in the energy efficiency of drying system. Thin-layer drying models have been used to describe the drying process of several agricultural products.
In the Chemical Engineering Laboratory of Afe Babalola University the PID controller of our tray drier system has been giving unsatisfactory performances. It is envisaged to replace the controller in future with an advanced one-model predictive controller. In order to carry out this efficiently a low dimensional lumped parameter is sought. Some model in literature are too complex (PDE’s) to be used for control purposes or do not match the mechanics of the tray drier of interest. However, the greatest drawback of the tray dryer is uneven drying because of poor airflow distribution in the drying chamber that can be removed by implementing some modification in the dryer design. (Katiyar et al., 2013). Thin layer drying kinetics is needed for design, operation and optimization of food crops dryers (Olawale et al., 2012). Therefore this project is aimed at developing lumped parameter model that will be suitable for control, since most of the models developed are too emperical, strongly non linear, and too complex to characterize tuning parameters in a control system.
1.2 Statement of Problem
The PID controller in our laboratory tray dryer has been giving unsatisfactory performances. It is envisaged to replace the controller in future with a more advanced one – model predictive controller. To be able to do this easily and efficiently, a low dimensional lumped parameter
3
model is sought. Some available in literature are either too complex (PDEs) to be used for control purposes or do not match the mechanics of the tray dryer of interest.
1.3 Scope of Study
The scope of study covers the modelling and simulation of a convective drying process of a thin slice layers of potato, using a tray dryer as the drying medium and MATLAB software will be employed as the simulation tool for this project.
1.4 Aim of Study
The aim of this work is to derive a mathematical model suitable for control. Potato will be dried in a tray dryer in order to define the essential drying parameters of a static thin layer of potato and plantain of known magnitude of thickness which could be used subsequently for control of these agricultural products and similar natural products in a ‘Tray dryer’.
1.5 Objectives
The following objectives are expected to be carried out:
i) Study and analyze existing mathematical models developed for tray dryer system drying some agricultural products
ii) Develop a mathematical model for a tray dryer using potato as the sample in the tray dryer.
iii) Simulation of the models using MATLAB software
iv) Compare the result with experimental data.
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1.6 Justification
Since most of the models developed are too emperical, strongly non linear, and too complex complex to characterize tuning parameters in a control system. This project is aimed at developing lumped parameter model that will be suitable for control.
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