Heat Transfer
in
Food Processing
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WIT
PRESS
International Series on Developments in Heat Transfer
Objectives
The Developments in Heat Transfer book Series publishes state-of-the-art
books and provides valuable contributions to the literature in the field of heat
transfer. The overall aim of the Series is to bring to the attention of the
international community recent advances in heat transfer by authors in
academic research and the engineering industry.
Research and development in heat transfer is of significant importance
to many branches of technology, not least in energy technology. Developments
include new, efficient heat exchangers, novel heat transfer equipment as well
as the introduction of systems of heat exchangers in industrial processes.
Application areas include heat recovery in the chemical and process industries,
and buildings and dwelling houses where heat transfer plays a major role.
Heat exchange combined with heat storage is also a methodology for
improving the energy efficiency in industry, while cooling in gas turbine
systems and combustion engines is another important area of heat transfer
research.
To progress developments within the field both basic and applied
research is needed. Advances in numerical solution methods of partial
differential equations, high-speed, efficient and cheap computers, advanced
experimental methods using LDV (laser-doppler-velocimetry), PIV (particle-
image-velocimetry) and image processing of thermal pictures of liquid
crystals, have all led to dramatic advances during recent years in the solution
and investigation of complex problems within the field.
The aims of the Series are achieved by contributions to the volumes
from invited authors only. This is backed by an internationally recognised
Editorial Board for the Series who represent much of the active research
worldwide. Volumes planned for the series include the following topics:
Compact Heat Exchangers, Engineering Heat Transfer Phenomena, Fins
and Fin Systems, Condensation, Materials Processing, Gas Turbine Cooling,
Electronics Cooling, Combustion-Related Heat Transfer, Heat Transfer in
Gas-Solid Flows, Thermal Radiation, the Boundary Element Method in Heat
Transfer, Phase Change Problems, Heat Transfer in Micro-Devices, Plate-
and-Frame Heat Exchangers, Turbulent Convective Heat Transfer in Ducts,
Enhancement of Heat Transfer and other selected topics.
Series Editor
B. Sundén
Lund Institute of Technology
Box 118
22100 Lund
Sweden
Associate Editors
E. Blums
Latvian Academy of Sciences
Latvia
C.A. Brebbia
Wessex Institute of Technology
UK
G. Comini
University of Udine
Italy
R.M. Cotta
COPPE/UFRJ,
Brazil
L. De Biase
University of Milan
Italy
G. De Mey
University of Ghent
Belgium
S. del Guidice
University of Udine
Italy
M. Faghri
University of Rhode Island
USA
P.J. Heggs
UMIST
UK
C. Herman
John Hopkins University
USA
D.B. Ingham
University of Leeds
UK
Y. Jaluria
Rutgers University
USA
S. Kotake
University of Tokyo
Japan
D.B. Murray
Trinity College Dublin
Ireland
K. Onishi
Ibaraki University
Japan
P.H. Oosthuizen
Queen’s University Kingston
Canada
W. Roetzel
Universtaet der Bundeswehr
Germany
B. Sarler
Nova Gorica Polytechnic
Slovenia
A.C.M. Sousa
University of New Brunswick
Canada
D.B. Spalding
CHAM
UK
J. Szmyd
University of Mining and Metallurgy
Poland
E. Van den Bulck
Katholieke Universiteit Leuven
Belgium
S. Yanniotis
Agricultural University of Athens
Greece
Heat Transfer
in
Food Processing
EDITORS
S.Yanniotis
Agricultural University of Athens, Greece
B. Sundén
Lund Institute of Technology, Sweden
Recent Developments and Applications
Published by
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British Library Cataloguing-in-Publication Data
A Catalogue record for this book is available
from the British Library
ISBN: 978-1-85312-932-2
ISSN: 1369-7331
Library of Congress Catalog Card Number: 2006940429
The texts of the papers in this volume were set
individually by the authors or under their supervision.
No responsibility is assumed by the Publisher, the Editors and Authors for any injury and/
or damage to persons or property as a matter of products liability, negligence or otherwise,
or from any use or operation of any methods, products, instructions or ideas contained in the
material herein. The Publisher does not necessarily endorse the ideas held, or views expressed
by the Editors or Authors of the material contained in its publications.
© WIT Press 2007
Printed in Great Britain by Cambridge Printing
All rights reserved. No part of this publication may be reproduced, stored in a retrieval
system, or transmitted in any form or by any means, electronic, mechanical, photocopying,
recording, or otherwise, without the prior written permission of the Publisher.
Editors:
S. Yanniotis
Agricultural University of Athens, Greece
B. Sundén
Lund Institute of Technology, Sweden
Contents
Preface xi
Chapter 1
Numerical modelling of heat transfer in the food industry – recent
developments and applications..................................................................... 1
K. Sardi & S. Yanniotis
1 Introduction .............................................................................................. 1
2 Finite difference (FD) methods ................................................................ 3
2.1 FD approaches by Taylor series expansion...................................... 5
2.2 FD approaches by energy balance.................................................... 8
2.3 Limitations of the FD approach ....................................................... 9
3 Finite element (FE) methods .................................................................... 9
4 Finite volume (FV) methods..................................................................... 15
5 Computational fluid dynamics (CFD) ...................................................... 17
5.1 Single-phase flow problems............................................................. 22
5.2 Two-phase flow problems................................................................ 24
6 Conclusions and outlook .......................................................................... 26
Chapter 2
Neural network applications in heat and mass transfer operations
in food processing .......................................................................................... 39
C.R. Chen, H.S. Ramaswamy & M. Marcotte
1 Introduction .............................................................................................. 39
2 Principles of a basic artificial neural network (ANN) model ................... 41
2.1 Neural network architecture............................................................. 42
2.2 Artificial neurons ............................................................................. 43
2.3 Learning rules................................................................................... 44
2.4 Advantages and limitations of neural networks ............................... 45
3 Developing neural networks..................................................................... 46
4 ANN applications in heat and mass transfer operations........................... 48
4.1 Predictions........................................................................................ 48
4.2 Optimization..................................................................................... 49
4.3 Control ............................................................................................. 49
4.4 Selected ANN examples in heat and mass transfer applications...... 49
5 Future trends............................................................................................. 56
Chapter 3
Freezing and thawing of foods – computation methods and thermal
properties correlation.................................................................................... 61
H. Schwartzberg, R.P. Singh & A. Sarkar
1 Engineering calculations........................................................................... 61
2 Freezing points ......................................................................................... 61
2.1 Freezing point depression ................................................................ 62
2.2 Bound water ..................................................................................... 62
3 Water and ice weight fractions ................................................................. 63
4 Effective heat capacities ........................................................................... 64
5 Enthalpies ................................................................................................. 65
5.1 Use of T
i
as T
R
.................................................................................. 66
5.2 Use of –40ºC as T
R
.......................................................................... 66
6 Departures from equilibrium .................................................................... 67
7 Volume changes ....................................................................................... 68
8 Food composition variation...................................................................... 68
9 Thermal conductivity................................................................................ 69
10 Freezing time estimation .......................................................................... 70
10.1 Thawing-time estimation.................................................................. 71
10.2 Precooling and subcooling ............................................................... 71
11 Heat transfer coefficients.......................................................................... 72
12 Unsteady-state freezing and thawing........................................................ 72
13 Explicit numerical solution of PDE.......................................................... 73
14 Implicit numerical solution of PDE.......................................................... 74
15 Lee’s method ............................................................................................ 75
16 Enthalpy step method ............................................................................... 75
16.1 Sample results for the enthalpy step method.................................... 76
17 Multidimensional problems...................................................................... 78
17.1 Enthalpy step method....................................................................... 78
17.2 Explicit, temperature step method.................................................... 82
17.3 Alternating-direction implicit (ADI) methods ................................. 82
18 Irregular shape and nonuniform composition........................................... 83
18.1 Coordinate transformation................................................................ 83
18.2 Finite element method...................................................................... 83
Chapter 4
Microwave and radio frequency in sterilization and pasteurization
applications..................................................................................................... 101
J. Tang & Tse V. Chow Ting Chan
1 Introduction .............................................................................................. 102
2 Basic principles of microwave and RF heating ........................................ 103
2.1 Mechanisms of microwave and RF heating ..................................... 103
2.2 Frequencies allocated for industrial heating applications ................ 104
2.3 Governing equations for electromagnetic waves ............................. 106
2.4 Electromagnetic wave propagation .................................................. 107
2.5 Penetration depth of microwave and RF waves in foods ................. 111
2.6 Effect of temperature on food dielectric properties.......................... 112
3 Microwave and RF heating systems......................................................... 115
3.1 Microwave heating systems ............................................................. 115
3.2 RF heating systems .......................................................................... 119
4 Review of research and industrial applications ........................................ 123
4.1 Microwave sterilization.................................................................... 123
4.2 Microwave pasteurization ................................................................ 126
4.3 RF heating ........................................................................................ 127
4.4 Bacterial considerations ................................................................... 130
4.5 Effect of microwaves on chemical reactions.................................... 133
5 New developments in microwave and RF sterilization research.............. 134
5.1 Chemical marker methods................................................................ 134
5.2 Fiber optic sensors............................................................................ 139
5.3 Computer simulation........................................................................ 142
Chapter 5
Ohmic heating: models and measurements................................................. 159
K. Samprovalaki, S. Bakalis & P.J. Fryer
1 Introduction .............................................................................................. 159
2 The fundamentals of ohmic heating ......................................................... 160
3 Commercial design of the ohmic process................................................. 161
4 Modelling ohmic heating.......................................................................... 162
4.1 Modelling approaches ...................................................................... 162
4.2 Development of modelling approaches............................................ 169
5 Experimental studies on ohmic heating.................................................... 170
5.1 Measurement of electrical conductivity ........................................... 170
5.2 Experimental measurements ............................................................ 172
5.3 Specification of correct electrodes and measurement methods........ 173
6 Applications of ohmic heating and electric fields .................................... 175
6.1 Microbial destruction ....................................................................... 175
6.2 Mass transfer enhancement .............................................................. 176
6.3 Ohmic pretreatment.......................................................................... 178
7 Conclusions .............................................................................................. 180
Chapter 6
Aseptic processing of liquid/particulate foods............................................. 187
N.G. Stoforos & H. Sawada
1 Introduction .............................................................................................. 187
2 Mathematical analysis .............................................................................. 189
2.1 Generalized solution for spherical particles with nonuniform
initial temperature heated in a variable temperature medium .......... 191
3 Study of aseptic processing of liquid/particulate foods............................ 196
3.1 Heating section................................................................................. 196
3.2 Holding section ................................................................................ 197
3.3 Cooling section................................................................................. 198
3.4 Sample calculations.......................................................................... 200
4 Conclusions .............................................................................................. 202
Chapter 7
Deep-fat frying ............................................................................................... 209
R.G. Moreira
1 Introduction .............................................................................................. 209
2 Mathematical models................................................................................ 210
2.1 Heat and mass balances models – the semi-empirical models ......... 210
2.2 DE models – the deterministic models............................................. 210
2.3 Multiphase porous media models – the mechanistic model............. 215
3 Conclusions .............................................................................................. 236
Chapter 8
Heat and mass transfer during baking ........................................................ 239
M. Marcotte
1 Introduction .............................................................................................. 240
2 Heat and mass transfer in the baking oven and within product................ 244
2.1 General description .......................................................................... 244
3 Physical, thermal and mass transfer properties......................................... 255
3.1 Thermophysical properties............................................................... 255
3.2 Mass diffusion and transfer properties ............................................. 256
4 Starchy products as bubble foods or cellular solids.................................. 257
4.1 Volume expansion kinetics .............................................................. 259
4.2 Modeling of volume expansion kinetics .......................................... 260
5 Conclusions .............................................................................................. 261
Index 267
Preface
Heat transfer is one of the most important and most common engineering disciplines
in food processing. There are many unit operations in the food industry where
steady or unsteady state heat transfer is taking place e.g. sterilization, dehydration,
freezing etc. Heat transfer in these operations is of primary importance and affects
the design of equipment as well as safety, nutritional and sensory aspects of the
product.
In applying heat transfer knowledge to food processing, one must take into
account that the food industry usually deals with difficult raw materials with irregular
shapes, in many cases of non-uniform and variable consistency, with physical
properties that may change during processing. Due to these complexities, the
unsteady state heat transfer differential equations can only be solved analytically
with several simplifying assumptions, while numerical solutions of these equations
can handle such complexities.
The chapters in this book deal mainly with heat transfer applications or methods
that have considerable physical property variations with temperature, e.g. freezing,
or methods that are not yet widely spread in the food industry, e.g. ohmic heating,
infrared radiation, or are less developed in the food engineering literature, e.g. deep-
fat frying or baking. The application of numerical methods has received special
attention with a separate chapter as well as emphasis in almost every chapter because
a substantial number of papers in food processing operations have been published
in recent years dealing with numerical solutions of heat transfer problems. It is
expected that because of the increased computational capabilities that are possible
today with high speed and low price computers, numerical solutions will be used in
an increasing range of food processing applications in the near future. A chapter on
artificial neural networks (ANN) has been included since ANN is a promising
alternative tool to conventional methods for modelling, optimization etc in cases
where a clear relationship between the variables is not known or the system is too
complex to be modelled with conventional mathematical methods.
We would like to thank the authors for their contributions. Without their effort
and expertise this book would not have been possible.
The Editors
2007
