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/
2
m
Pwo
Vapor pressure N/
2
m
*
P
Vapor pressure N/
2
m
Nu Nusselt number No unit
Pr Prandtl number No unit
Re Reynolds number No unit
Sc Schmidt number No unit
P Total pressure N /
2
m
bulk Pw
Partial pressure/vapor pressure
of component
2
ms
kg surface Pw
Partial pressure of water vapor
in the air at the solid interface
2
ms
kg air Pw
Partial vapor of water vapor in
air
2
ms
kg
xi
Symbol
Meaning
Density
Units
3 m
kg
air
Density of air
3 m
kg
k Mass transfer coefficient
s
m
c
k
Mass transfer for a convective
driving force
s
m
p k
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
air k
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.
4
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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