MATHEMATICAL MODELLING OF SOLAR DRYING OF MANGO SLICES BY EL-AMIN OMDA ...

192 Pages·2008·0.89 MB·English

MATHEMATICAL MODELLING OF SOLAR
DRYING OF MANGO SLICES

BY
EL-AMIN OMDA MOHAMED AKOY
B.Sc. (Honours) Agricultural Sciences
University of Gezira, 1995
M.Sc. (Agric.) 2000
University of Khartoum

A Thesis Submitted To the University of Khartoum in
Fulfillment of the Requirements for the Degree of
Doctor of Philosophy in Agriculture

Supervisor: Dr. Mohamed Ayoub Ismail
Co-supervisor: Dr. El-Fadil Adam Ahmed

DEPARTMENT OF AGRICULTURAL ENGINEERING
FACULTY OF AGRICULTURE
UNIVERSITY OF KHARTOUM
July, 2007
DEDICATION

This work is dedicated to the soul of my late brother
El-Nour Omda Mohamed Akoy
TABLE OF CONTENTS

Page
ACKNOWLEDGEMENT i
ENGLISH ABSTRACT ii
ARABIC ABSTRACT vi
LIST OF TABLES ix
LIST OF FIGURES xi
LIST OF PLATES xiii
LIST OF SYMBOLS xiv
CHAPTER ONE: INTRODUCTION 1
CHAPTER TWO: LITERATURE REVIEW 5
2.1 The Concept of Drying and Drying Mechanism 5
2.1.1 The constant rate period 7
2.1.2 The falling rate period 8
2.1.2.1 Effective diffusion coefficient 12
2.2 Parameters Affecting the Drying Rate 13
2.2.1 Drying air temperature 14
2.2.2 Drying air relative humidity 14
2.2.3 Drying air flow rate 15
2.2.4 Product moisture content 16
2.2.5 Product drying constant 17
2.3 Equilibrium Moisture Content (EMC) and Water Activity 21
2.3.1Moisture sorption isotherms determination 23
2.4 Layer Drying 24
2.4.1 Thin layer drying: 24
2.4.2 Deep bed (layer) drying 25
Page
2.5 Economical Importance of Dried Fruits and Vegetables 26
2.5.1 Solar drying of fruits and vegetables 28
2.5.2 Mango fruit in Sudan 29
2.6 Classification of Drying Methods 33
2.6.1 Unheated air drying 35
2.6.2 Heated air drying 35
2.6.2.1 Fossil dryer 36
2.6.2.2 Electrical drying 36
2.6.3 Solar drying 36
2.6.3.1 Types of solar dryers 38
2.7 Modelling and Simulation and Design of Drying Processes 41
2.7.1 Mathematical modelling of thin layer drying 42
2.7.1.1 Theoretical Models 44
2.7.1.2 Semi-theoretical models 45
2.7.1.3 Empirical models 47
2.8 Mathematical Description of Sorption Isotherms 47
CHAPTER THREE: MATERIALS AND METHODS 50
3.1 Testing Three Thin-layer Drying Models for Mango Slices 50
3.1.1 Assumptions 50
3.1.2 Manipulation of the tested three drying models 50
3.2 Preliminary Investigations on Drying Kinetics of Mango 57
Slices
3.2.1 Materials and equipment 57
3.2.1.1 Materials 57
3.2.1.2 Equipment 57
Page
3.2.2 Methods 58
3.2.2.1 Fresh mango (physical analysis) 58
3.2.2.2 Moisture content determination 59
3.2.3 The experimental procedure 59
3.2.4 Chemical analysis (quality attributes) 61
3.2.4.1 pH of fresh mango 61
3.2.4.2 Total sugar and reducing sugar 61
3.2.4.3 Non-enzymatic browning 62
3.2.4.4 Rehydration ratio (Reconstitution ratio) 63
3.3 Design and Construction of a Solar Dryer for Mango Slices 63
3.3.1 Design of the solar dryer 63
3.3.3.1 Design procedure 64
3.3.3.2 Design calculation 65
3.3.2 Construction of a cabinet-type solar dryer 70
3.3.2.1 Materials and Methods 70
3.3.2.2 Preliminary testing of the dryer 76
3.3.2.3 Solar drying experiments 77
3.3.2.4 Thin-layer solar drying experiments 79
3.3.3 Mathematical modelling of solar drying of mango slices 80
3.3.4 Statistical validation of the selected models 80
3.3.4 Simulation of thin-layer drying of mango slices 81
3.4.Moisture Sorption Behaviour of Solar-dried Mango Slice 83
3.4.1 Materials and Methods 83
3.4.1.1Materials 83
3.4.1.2 Methods 83
3.4.2 Fitting sorption isotherms 86
Page
3.4.3 Statistical validation of selected sorption models 88
CHAPTER FOUR: RESULTS AND DISCUSSIONS 89
4.1 Preliminary Investigations on Drying Kinetics of Mango 89
Slices
4.1.1 Effect of drying temperatures on drying kinetics of mango 89
slices
4.1.2 Effect of drying air temperature on quality attributes of 93
mango slices
4.1.3 Effect of drying temperatures on selected models 97
4.1.4 Effect of drying temperature on drying constant 97
4.1.5 Effect of drying temperature on effective diffusivity 102
4.1.6. Statistical validation of the tested models 104
4.2 Solar Drying of Mango Slices 108
4.2.1 Drying performance of the constructed solar dryer 108
4.2.2 Solar drying characteristics of mango slices 113
4.2.3 Mathematical modeling of solar drying of mango slices 117
4.3 Moisture Sorption Characteristics of Solar-Dried Mango 124
Slices
4.3.1 Curve fitting of sorption isotherms of solar dried mango 126
slices
CHAPTER FIVE: CONCLUSIONS AND 130
RECOMMENDATIONS
5.1 Conclusions 130
5.2 Recommendations 131
REFERENCES 132
APPENDICES 158
ACKNOWLEDGEMENT

I would like to express my deepest appreciation and sincere
gratitude to my supervisor Dr. Mohamed Ayoub Ismail and my co-
supervisor Dr. El-Fadil Adam Ahmed for their close and careful
supervision, continuous guidance and encouragement throughout the
course of this study. Also, I would like to express my appreciation and
sincere gratitude to my advisors at the Institute of Agricultural
Engineering, University of Goettingen, Germany, Prof. Dr. Wolfgang
Leucke and Dr. Dieter von Hoersten for their careful supervision,
endless patience and continuous follow-up and encouragement during
my 6-month research stay.
Thanks are extended to the very nice colleagues at the Institute
of Agricultural Engineering, University of Goettingen. Many thanks
are also extended to my colleagues and staff members of Agric. Eng.
Department, Faculty of Agriculture, University of Khartoum.
I gratefully acknowledge the German Academic Exchange
service (DAAD) for granting in-country scholarship and short-term
research scholarship in Germany. Also University of Zalingei is
highly acknowledged for granting the scholarship, which made this
study possible.
Finally, my thanks and appreciation to my family, without
whom this study would not be accomplished.

i
ABSTRACT

Three experiments were conducted through the cooperation
among the Department of Agricultural Engineering, Faculty of
Agriculture, University of Khartoum, Sudan and the Food Research
Centre, Ministry of Science and Technology, Sudan and the Institute
of Agricultural Engineering, University of Goettingen, Germany to
study thin layer solar drying of mango and the related quality
attributes resulted from the drying process and sorption isotherms of
solar dried mango slices.
The first experiment was conducted at the Food Research
Centre under controlled conditions using an air oven. Only the
influence of drying temperatures at 50°C, 60°C, 70°C, 80°C and 90°C
on many drying behaviour and quality were studied. The change in
mass of mango slices was recorded continuously at specified intervals
of 30 min during the experiment using a sensitive balance. The desired
drying air temperature was regulated by means of temperature
controller and checked using a thermometer. Quality attributes studied
included total sugar, reducing sugar, rehydration ratio and non-
enzymatic browning. The total sugar and reducing sugar were
evaluated by titration method whereas non-enzymatic browning by
extraction method. Drying curves obtained from the experimental data
were then fitted to three well-known semi-empirical thin-layer drying
models namely; Lewis model, Page model and Henderson and Pabis
model. Model constants and coefficients were determined by
nonlinear regression method. Microsoft Excel spreadsheet software
was used to simulate drying characteristics of mango slices.
ii
Results revealed that in order to produce high quality mango
product, higher temperatures of 70°C to 80°C have to be applied as
the optimum drying temperature. Results indicated that drying
constant (k) increases as drying temperature increases. The effective
moisture diffusivity (D ) varied from 1.87 × 10-6cm2/sec to 3.67 × 10-
eff
6cm2/sec in temperature range from 50°C to 90°C. Also, the effective
moisture diffusivity (D ) increases as drying temperature increases.
eff
The drying took place in the falling rate period and increasing air
temperature lessens drying times. All the models were validated using
statistical parameters namely; coefficient of determination (R2), sum
of square error (SSE), root mean square error (RMSE) and reduced
chi-square (χ2). Among the drying models investigated, the Page
model satisfactory described the drying behaviour of mango slices.
In the second experiment, a natural convection solar dryer was
designed and constructed to dry mango slices. The constructed dryer
consisted of a drying chamber and a solar collector combined in one
unit. Inside the drying chamber there were two movable mesh wire
trays for easy loading and unloading of the mango slices.
In order to investigate the dryer performance several test runs
were conducted at the Workshop of Department of Agricultural
Engineering, Faculty of Agriculture, University of Khartoum. In these
tests, drying air and ambient air parameters were recorded
continuously at specified intervals of 30 min. Thermocouples
connected to a data logger were used to measure temperature whereas
digital hygrometers were used to measure relative humidity. To study
solar drying characteristics of mango slices, the change in mass of
mango slices was recorded at 30 minutes intervals until reaching
constant weight using a sensitive balance. The same tested drying
iii
models used in the first experiment were employed for the
experimental data of the second experiment. A computer programme
was written using Turbo Pascal programming language, version 7 to
simulate the thin layer solar drying of mango slices.
Results revealed that the dryer attained a temperature 20ºC
higher than ambient temperature. The heated air temperature was
higher than ambient one and the difference was found to be significant
(P < 0.05). The heated air relative humidity was lower than ambient
one and the difference was found to be significant (P < 0.05).
Furthermore results revealed that, the dryer attained a maximum
temperature of 70ºC, which is considered as the optimum temperature
for mango slices drying.
Of the three tested drying models, Page model shows close
agreement between predicted and measured moisture contents.
In the third experiment water sorption behaviour of solar-dried
mango slices at three temperatures of 20°C, 30°C and 40°C for a
water activity (a ) range of 0.111 to 0.813 was conducted at the
w
Institute of Agricultural Engineering, University of Goettingen. The
sorption isotherms of solar dried mango slices were determined by the
standard static gravimetric method; using saturated salt solutions
inside air-tight glass jars to maintain a fixed relative humidity. To
maintain the constant temperatures, incubators were used. Solar dried
samples were weighed at intervals of two days using a sensitive
balance until constant weight was reached. The experimental results
were fitted to two well-known mathematical sorption models namely;
BET model and GAB model. The validation of the two selected
models was done by using a statistical parameter namely; mean
relative percentage deviation (% P). Microsoft Excel spreadsheet
iv