DK3951_half 8/3/05 12:08 PM Page 1 ThermalFoodProcessingFOOD SCIENCE AND TECHNOLOGYA Series of Monographs, Textbooks, and Reference BooksEditorial Advisory BoardGustavo V. Barbosa-Cnovas Washington State UniversityPullmanP. Michael Davidson University of TennesseeKnoxvilleMark Dreher McNeil Nutritionals, New Brunswick, NJRichard W. Hartel University of WisconsinMadisonLekh R. Juneja Taiyo Kagaku Company, JapanMarcus Karel Massachusetts Institute of TechnologyRonald G. Labbe University of MassachusettsAmherstDaryl B. Lund University of WisconsinMadisonDavid B. Min The Ohio State UniversityLeo M. L. Nollet Hogeschool Gent, BelgiumSeppo Salminen University of Turku, FinlandJohn H. Thorngate III Allied Domecq Technical Services, Napa, CAPieter Walstra Wageningen University, The NetherlandsJohn R. Whitaker University of CaliforniaDavisRickey Y. Yada University of Guelph, Canada76. Food Chemistry: Third Edition, edited by Owen R. Fennema77. Handbook of Food Analysis: Volumes 1 and 2, edited by Leo M. L. Nollet78. Computerized Control Systems in the Food Industry, edited byGauri S. Mittal79. Techniques for Analyzing Food Aroma, edited by Ray Marsili80. Food Proteins and Their Applications, edited by Srinivasan Damodaran and Alain Paraf81. Food Emulsions: Third Edition, Revised and Expanded, edited byStig E. Friberg and Kre Larsson82. Nonthermal Preservation of Foods, Gustavo V. Barbosa-Cnovas, Usha R. Pothakamury, Enrique Palou, and Barry G. Swanson83. Milk and Dairy Product Technology, Edgar Spreer84. Applied Dairy Microbiology, edited by Elmer H. Marth and James L. Steele85. Lactic Acid Bacteria: Microbiology and Functional Aspects,Second Edition, Revised and Expanded, edited by Seppo Salminen and Atte von Wright86. Handbook of Vegetable Science and Technology: Production,Composition, Storage, and Processing, edited by D. K. Salunkheand S. S. KadamDK3951_series.qxd 11/3/05 10:33 AM Page 187. Polysaccharide Association Structures in Food, edited byReginald H. Walter88. Food Lipids: Chemistry, Nutrition, and Biotechnology, edited byCasimir C. Akoh and David B. Min89. Spice Science and Technology, Kenji Hirasa and Mitsuo Takemasa90. Dairy Technology: Principles of Milk Properties and Processes, P. Walstra, T. J. Geurts, A. Noomen, A. Jellema, and M. A. J. S. van Boekel91. Coloring of Food, Drugs, and Cosmetics, Gisbert Ottersttter92. Listeria, Listeriosis, and Food Safety: Second Edition, Revised and Expanded, edited by Elliot T. Ryser and Elmer H. Marth93. Complex Carbohydrates in Foods, edited by Susan Sungsoo Cho,Leon Prosky, and Mark Dreher94. Handbook of Food Preservation, edited by M. Shafiur Rahman95. International Food Safety Handbook: Science, InternationalRegulation, and Control, edited by Kees van der Heijden, Maged Younes, Lawrence Fishbein, and Sanford Miller96. Fatty Acids in Foods and Their Health Implications: Second Edition, Revised and Expanded, edited by Ching Kuang Chow97. Seafood Enzymes: Utilization and Influence on PostharvestSeafood Quality, edited by Norman F. Haard and Benjamin K. Simpson98. Safe Handling of Foods, edited by Jeffrey M. Farber and Ewen C. D. Todd99. Handbook of Cereal Science and Technology: Second Edition,Revised and Expanded, edited by Karel Kulp and Joseph G. Ponte, Jr.100. Food Analysis by HPLC: Second Edition, Revised and Expanded,edited by Leo M. L. Nollet101. Surimi and Surimi Seafood, edited by Jae W. Park102. Drug Residues in Foods: Pharmacology, Food Safety, and Analysis, Nickos A. Botsoglou and Dimitrios J. Fletouris103. Seafood and Freshwater Toxins: Pharmacology, Physiology, and Detection, edited by Luis M. Botana104. Handbook of Nutrition and Diet, Babasaheb B. Desai105. Nondestructive Food Evaluation: Techniques to AnalyzeProperties and Quality, edited by Sundaram Gunasekaran106. Green Tea: Health Benefits and Applications, Yukihiko Hara107. Food Processing Operations Modeling: Design and Analysis,edited by Joseph Irudayaraj108. Wine Microbiology: Science and Technology, Claudio Delfini and Joseph V. Formica109. Handbook of Microwave Technology for Food Applications, edited by Ashim K. Datta and Ramaswamy C. Anantheswaran110. Applied Dairy Microbiology: Second Edition, Revised and Expanded, edited by Elmer H. Marth and James L. SteeleDK3951_series.qxd 11/3/05 10:33 AM Page 2111. Transport Properties of Foods, George D. Saravacos and Zacharias B. Maroulis112. Alternative Sweeteners: Third Edition, Revised and Expanded,edited by Lyn OBrien Nabors113. Handbook of Dietary Fiber, edited by Susan Sungsoo Cho and Mark L. Dreher114. Control of Foodborne Microorganisms, edited by Vijay K. Juneja and John N. Sofos115. Flavor, Fragrance, and Odor Analysis, edited by Ray Marsili116. Food Additives: Second Edition, Revised and Expanded, edited by A. Larry Branen, P. Michael Davidson, Seppo Salminen,and John H. Thorngate, III117. Food Lipids: Chemistry, Nutrition, and Biotechnology: Second Edition, Revised and Expanded, edited by Casimir C. Akoh and David B. Min118. Food Protein Analysis: Quantitative Effects on Processing, R. K. Owusu-Apenten119. Handbook of Food Toxicology, S. S. Deshpande120. Food Plant Sanitation, edited by Y. H. Hui, Bernard L. Bruinsma, J. Richard Gorham, Wai-Kit Nip, Phillip S. Tong, and Phil Ventresca121. Physical Chemistry of Foods, Pieter Walstra122. Handbook of Food Enzymology, edited by John R. Whitaker, Alphons G. J. Voragen, and Dominic W. S. Wong123. Postharvest Physiology and Pathology of Vegetables: Second Edition, Revised and Expanded, edited by Jerry A. Bartzand Jeffrey K. Brecht124. Characterization of Cereals and Flours: Properties, Analysis, and Applications, edited by Gnl Kaletun and Kenneth J. Breslauer125. International Handbook of Foodborne Pathogens, edited byMarianne D. Miliotis and Jeffrey W. Bier126. Food Process Design, Zacharias B. Maroulis and George D. Saravacos127. Handbook of Dough Fermentations, edited by Karel Kulp and Klaus Lorenz128. Extraction Optimization in Food Engineering, edited byConstantina Tzia and George Liadakis129. Physical Properties of Food Preservation: Second Edition, Revised and Expanded, Marcus Karel and Daryl B. Lund130. Handbook of Vegetable Preservation and Processing, edited by Y. H. Hui, Sue Ghazala, Dee M. Graham, K. D. Murrell, and Wai-Kit Nip131. Handbook of Flavor Characterization: Sensory Analysis,Chemistry, and Physiology, edited by Kathryn Deibler and Jeannine Delwiche132. Food Emulsions: Fourth Edition, Revised and Expanded, edited by Stig E. Friberg, Kare Larsson, and Johan SjoblomDK3951_series.qxd 11/3/05 10:33 AM Page 3133. Handbook of Frozen Foods, edited by Y. H. Hui, Paul Cornillon, Isabel Guerrero Legarret, Miang H. Lim, K. D. Murrell, and Wai-Kit Nip134. Handbook of Food and Beverage Fermentation Technology, edited by Y. H. Hui, Lisbeth Meunier-Goddik, Ase Solvejg Hansen,Jytte Josephsen, Wai-Kit Nip, Peggy S. Stanfield, and Fidel Toldr135. Genetic Variation in Taste Sensitivity, edited by John Prescott and Beverly J. Tepper136. Industrialization of Indigenous Fermented Foods: Second Edition,Revised and Expanded, edited by Keith H. Steinkraus137. Vitamin E: Food Chemistry, Composition, and Analysis, Ronald Eitenmiller and Junsoo Lee138. Handbook of Food Analysis: Second Edition, Revised and Expanded, Volumes 1, 2, and 3, edited by Leo M. L. Nollet139. Lactic Acid Bacteria: Microbiological and Functional Aspects:Third Edition, Revised and Expanded, edited by Seppo Salminen,Atte von Wright, and Arthur Ouwehand140. Fat Crystal Networks, Alejandro G. Marangoni141. Novel Food Processing Technologies, edited by Gustavo V. Barbosa-Cnovas, M. Soledad Tapia, and M. Pilar Cano142. Surimi and Surimi Seafood: Second Edition, edited by Jae W. Park143. Food Plant Design, Antonio Lopez-Gomez; Gustavo V. Barbosa-Cnovas144. Engineering Properties of Foods: Third Edition, edited by M. A. Rao, Syed S.H. Rizvi, and Ashim K. Datta145. Antimicrobials in Food: Third Edition, edited by P. Michael Davidson, John N. Sofos, and A. L. Branen146. Encapsulated and Powdered Foods, edited by Charles Onwulata147. Dairy Science and Technology: Second Edition, Pieter Walstra,Jan T. M. Wouters and Tom J. Geurts148. Food Biotechnology, Second Edition, edited by Kalidas Shetty, Gopinadhan Paliyath, Anthony Pometto and Robert E. Levin149. Handbook of Food Science, Technology, and Engineering - 4Volume Set, edited by Y. H. Hui150. Thermal Food Processing: New Technologies and Quality Issues,edited by Da-Wen Sun151. Aflatoxin and Food Safety, edited by Hamed K. Abbas152. Food Packaging: Principles and Practice, Second Edition, Gordon L. RobertsonDK3951_series.qxd 11/3/05 10:33 AM Page 4DK3951_title 8/3/05 12:07 PM Page 1 ThermalFoodProcessingEdited byDa-Wen SunA CRC title, part of the Taylor & Francis imprint, a member of theTaylor & Francis Group, the academic division of T&F Informa plc.Boca Raton London New YorkPublished in 2006 byCRC PressTaylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300Boca Raton, FL 33487-2742 2006 by Taylor & Francis Group, LLCCRC Press is an imprint of Taylor & Francis GroupNo claim to original U.S. Government worksPrinted in the United States of America on acid-free paper10 9 8 7 6 5 4 3 2 1International Standard Book Number-10: 1-57444-628-2 (Hardcover) International Standard Book Number-13: 978-1-57444-628-9 (Hardcover) Library of Congress Card Number 2005048598This book contains information obtained from authentic and highly regarded sources. Reprinted material isquoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable effortshave been made to publish reliable data and information, but the author and the publisher cannot assumeresponsibility for the validity of all materials or for the consequences of their use.No part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic,mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, andrecording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www.copyright.com(http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC) 222 Rosewood Drive,Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registrationfor a variety of users. For organizations that have been granted a photocopy license by the CCC, a separatesystem of payment has been arranged.Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used onlyfor identification and explanation without intent to infringe.Library of Congress Cataloging-in-Publication DataThermal food processing : new technologies and quality issues / edited by Da-Wen Sun.p. cm. (Food science and technology ; 149)Includes bibliographical references and index.ISBN 1-57444-628-21. Food--Storage. 2. Food--Preservation. I. Sun Da-Wen. II. Series.TX601.T43 2005664'.028--dc22 2005048598Visit the Taylor & Francis Web site at http://www.taylorandfrancis.comand the CRC Press Web site at http://www.crcpress.comTaylor & Francis Group is the Academic Division of Informa plc.DK3951_Discl.fm Page 1 Thursday, November 3, 2005 11:31 AM Preface Thermal processing is one of the most important processes in the food industry.The concept of thermal processing is based on heating foods for a certain lengthof time at a certain temperature. The challenge of developing advanced thermalprocessing for the food industry is continuing in line with the demand forenhanced food safety and quality, because associated with thermal processing isalways some undesirable degradation of heat-sensitive quality attributes. There-fore, this book covers a comprehensive review of the latest developments inthermal food processing technologies, stresses topics vital to the food industrytoday, and pinpoints the trends in future research and development. This book iswritten for food engineers and technologists in the food industry. It will alsoserve as an essential and complete reference source to undergraduate and post-graduate students and researchers in universities and research institutions.The contents of the book are divided into three parts: modeling of thermalfood processes, quality and safety of thermally processed foods, and innovationsin thermal food processes.Part I deals with topics relating to modeling, which is needed for the designand optimization of thermal processing of foods. This part begins with Chapter1 on thermal physical properties of foods, which contains fundamental data andequations used in modeling. The recent developments in heat and mass transferduring thermal processing are reviewed in Chapter 2. The remaining three chap-ters discuss innovative modeling techniques, including simulation using deter-ministic models (Chapter 3), modeling using an articial neural network (Chapter4), and computational uid dynamics (Chapter 5), which have been increasinglyapplied in the food industry.Maintenance of high quality and safety of thermally processed foods has beena major challenge in food processing. Part II presents recent R&D in this area.This part consists of nine chapters, each of which describes one type of foodproduct. The rst three chapters address respectively the quality and safety ofthermally processed meat (Chapter 6), poultry (Chapter 7), and shery products(Chapter 8). Dairy products are dealt with in Chapter 9, with ultra-high-temperature(UHT) milk being a separate chapter, as UHT is the most common thermal treat-ment technique for milk (Chapter 10). Chapter 11 gives the recent and potentialfuture development in thermal processing of canned foods, which remains the mostuniversal and economic method for preserving foods with a long shelf life. In recentyears, ready meals have shown high rates of growth, indicating the importance ofinnovation in thermal processing technology to cater for development of new foodproducts, which is discussed in Chapter 12. Finally, this part is concluded with achapter on quality and safety of thermally processed vegetables (Chapter 13). DK3951_C000.fm Page v Monday, October 24, 2005 11:00 AM Various alternative thermal processing technologies have been developed inthe past. These innovations demonstrate the potentials for their applications inthe food industry to increase processing efciency, enhance product quality, andimprove food safety. Part III addresses in detail these innovations. Chapter 14covers the ohmic heating technique, which has been subjected to intensiveresearch work in the past two decades as a promising technology for new high-quality products. Using radio frequency (RF) energies or infrared rays to heatfoods is a fast and effective thermal processing technique that results in shorttreatment times preferred for maintaining high quality. These techniques are respec-tively presented in Chapters 15 and 16. Furthermore, innovations by combiningpressure and pH with thermal processing are described in Chapters 17 and 18. Lastbut not least, the use of timetemperature integrators (TTIs) to evaluate and controlthermal processes is discussed in the nal chapter of this book (Chapter 19).In this book, each chapter is written by an international expert (or experts),presenting thorough research results and critical reviews of one aspect of therelevant issue and including a comprehensive list of recently published literature.It should therefore provide valuable sources of information for further researchand developments for the food processing industry. DK3951_C000.fm Page vi Monday, October 24, 2005 11:00 AM The Editor Born in Southern China, ProfessorDa-Wen Sun is an internationally recog-nized gure for his leadership in foodengineering research and education. Hismain research activities include cooling,drying, and refrigeration processes andsystems, quality and safety of food prod-ucts, bioprocess simulation and optimiza-tion, and computer vision technology.Especially, his innovative work on vacuumcooling of cooked meats, pizza qualityinspection by computer vision, and ediblelms for shelf-life extension of fruit andvegetables has been widely reported in national and international media. Resultsof his work have been published in over 150 peer reviewed journal papers andmore than 200 conference papers.Dr. Sun received rst-class honors B.Sc. and M.Sc. degrees in mechanicalengineering and a Ph.D. degree in chemical engineering in China before workingin various universities in Europe. Dr. Sun became the rst Chinese to be perma-nently employed in an Irish University when he was appointed college lecturerat National University of Ireland, Dublin (University College Dublin) in 1995,and was then promoted to senior lecturer. Dr. Sun is now a professor and directorof the Food Refrigeration and Computerised Food Technology Research Groupat the Department of Biosystems Engineering, University College Dublin.As a leading educator in food engineering, Professor Sun has signicantlycontributed to the eld of food engineering. He has trained many Ph.D. students,who have made their own contributions to the industry and academia. ProfessorSun has also given lectures on advances in food engineering on a regular basisto academic institutions internationally and delivered keynote speeches at inter-national conferences. As a recognized authority in food engineering, he has beenconferred adjunct/visiting/consulting professorships from ten top universities inChina, including Zhejiang University, Shanghai Jiao Tong University, HarbinInstitute of Technology, China Agricultural University, South China Universityof Technology, and Southern Yangtze University. In recognition of his signicantcontribution to food engineering worldwide, the International Commission ofAgricultural Engineering (CIGR) awarded him the CIGR Merit Award in 2000,and the Institution of Mechanical Engineers (IMechE) based in the U.K. awardedhim Food Engineer of the Year 2004. DK3951_C000.fm Page vii Monday, October 24, 2005 11:00 AM Professor Sun is a fellow of the Institution of Agricultural Engineers. He hasalso received numerous awards for teaching and research excellence, includingtwice receiving the President Research Award of University College Dublin. Heis chair of CIGR Section VI on Postharvest Technology and Process Engineering,guest editor of Journal of Food Engineering and Computers and Electronics inAgriculture , and editorial board member for the Journal of Food Engineering ,the Journal of Food Process Engineering , and the Czech Journal of Food Sciences .He is also a chartered engineer registered in the U.K. Engineering Council. DK3951_C000.fm Page viii Monday, October 24, 2005 11:00 AM Contributors Jos Manuel Gallardo Abun Instituto de Investigaciones Marinas (CSIC)Vigo, Spain Jasim Ahmed Department of Food ScienceMcGill UniversitySte-Anne-de-Bellevue, Canada Ins de Castro Department of Biological EngineeringUniversity of MinhoBraga, Portugal C.R. Chen Agriculture and Agri-Food CanadaQuebec, Canada Xiao Dong Chen Department of Chemistry and Materials EngineeringUniversity of AucklandAuckland, New Zealand N. Datta School of Land and Food SciencesUniversity of QueenslandQueensland, Australia Paul L. Dawson Food Science and Human Nutrition DepartmentClemson UniversityClemson, South Carolina H.C. Deeth School of Land and Food SciencesUniversity of QueenslandQueensland, Australia A.E. Delgado Food Refrigeration and Computerised Food Technology Research GroupUniversity College DublinEarlsfort TerraceDublin, Ireland P.S. Fernndez Universidad Politcnica de CartagenaCartagena, Murcia, Spain A.L. Kelly Department of Food and Nutritional SciencesUniversity College CorkCork, Ireland Sunil Mangalassary Food Science and Human Nutrition DepartmentClemson UniversityClemson, South Carolina Pamela Manzi Istituto Nazionale di Ricerca per gli Alimenti e la NutrizioneRoma, Italy Weijie Mao Tokyo University of Marine Science and TechnologyTokyo, Japan DK3951_C000.fm Page ix Monday, October 24, 2005 11:00 AM Antonio Martnez Instituto de Agroqumica y Tecnologa de AlimentosValencia, Spain Isabel Medina Mndez Instituto de Investigaciones Marinas (CSIC)Vigo, Spain M.J. Ocio Universidad de ValenciaValencia, Spain Takashi Okazaki Hiroshima Prefectural Food Technology Research CenterHiroshima, Japan Alfredo Palop Departamento de Ingeniera de Alimentos y del Equipamiento AgrcolaUniversidad Politcnica de CartagenaCartagena, Spain Laura Pizzoferrato Istituto Nazionale di Ricerca per gli Alimenti e la NutrizioneRoma, Italy H.S. Ramaswamy Department of Food Science and Agricultural ChemistryMcGill UniversityQuebec, Canada D. Rodrigo Instituto de Agroqumica y Tecnologa de AlimentosValencia, Spain A.C. Rubiolo Instituto de Desarrollo Tecnolgico para la Industria Qumica (INTEC)Universidad Nacional del Litoral (UNL)Consejo Nacional de Investigaciones Cientcas y Tcnicas (CONICET)Santa Fe, Argentina Noboru Sakai Department of Food Science and TechnologyTokyo University of Marine Science and TechnologyTokyo, Japan Marcos Sanchez Department of Food Science and TechnologyUniversity of NebraskaLincolnLincoln, Nebraska Brian W. Sheldon North Carolina State UniversityRaleigh, North Carolina U.S. Shivhare Department of Chemical Engineering and TechnologyPanjab UniversityChandigarh, India Da-Wen Sun University College DublinEarlsfort TerraceDublin, Ireland Kanichi Suzuki Department of Applied Biological ScienceHiroshima UniversityKagamiyama Higashi-Hiroshima, Japan DK3951_C000.fm Page x Monday, October 24, 2005 11:00 AM Arthur A. Teixeira Agricultural and Biological Engineering DepartmentUniversity of FloridaGainesville, Florida Jos Antnio Teixeira Department of Biological EngineeringUniversity of MinhoBraga, Portugal Harshavardhan Thippareddi Department of Food Science and TechnologyUniversity of NebraskaLincolnLincoln, Nebraska Gary Tucker Department of Food Manufacturing TechnologiesCampden & Chorleywood Food Research AssociationChipping Campden, Gloucestershire, United Kingdom Antnio Augusto Vicente Department of Biological EngineeringUniversity of MinhoBraga, Portugal Lijun Wang Department of Biological Systems EngineeringUniversity of NebraskaLincolnLincoln, Nebraska Z. Jun Weng FMC Technologies, Inc.Madera, California Yanyun Zhao Department of Food Science and TechnologyOregon State UniversityCorvallis, Oregon DK3951_C000.fm Page xi Monday, October 24, 2005 11:00 AM DK3951_C000.fm Page xii Monday, October 24, 2005 11:00 AM Contents Part I: Modeling of Thermal Food Processes Chapter 1 Thermal Physical Properties of Foods..................................................................3 A.E. Delgado, Da-Wen Sun, and A.C. Rubiolo Chapter 2 Heat and Mass Transfer in Thermal Food Processing.......................................35 Lijun Wang and Da -W en Sun Chapter 3 Simulating Thermal Food Processes Using Deterministic Models ...................73 Arthur A. Teixeira Chapter 4 Modeling Food Thermal Processes Using Articial Neural Networks ...............................................................................................107 C.R. Chen and H.S. Ramaswamy Chapter 5 Modeling Thermal Processing Using Computational Fluid Dynamics (CFD) .....................................................................................133 Xiao Dong Chen Part II: Quality and Safety of ThermallyProcessed Foods Chapter 6 Thermal Processing of Meat Products .............................................................155 Harshavardhan Thippareddiand Marcos Sanchez DK3951_C000.fm Page xiii Monday, October 24, 2005 11:00 AM Chapter 7 Thermal Processing of Poultry Products..........................................................197 Paul L. Dawson, Sunil Mangalassary,and Brian W. Sheldon Chapter 8 Thermal Processing of Fishery Products..........................................................235 Isabel Medina Mndez and Jos Manuel Gallardo Abun Chapter 9 Thermal Processing of Dairy Products.............................................................265 A.L. Kelly, N. Datta, and H.C. Deeth Chapter 10 UHT Thermal Processing of Milk....................................................................299 Pamela Manzi and Laura Pizzoferrato Chapter 11 Thermal Processing of Canned Foods..............................................................335 Z. Jun Weng Chapter 12 Thermal Processing of Ready Meals................................................................363 Gary Tucker Chapter 13 Thermal Processing of Vegetables....................................................................387 Jasim Ahmed and U.S. Shivhare Part III: Innovations in Thermal Food Processes Chapter 14 Ohmic Heating for Food Processing ................................................................425 Antnio Augusto Vicente, Ins de Castro, and Jos Antnio Teixeira Chapter 15 Radio Frequency Dielectric Heating ................................................................469 Yanyun Zhao Chapter 16 Infrared Heating ................................................................................................493 Noboru Sakai and Weijie Mao DK3951_C000.fm Page xiv Monday, October 24, 2005 11:00 AM Chapter 17 Pressure-Assisted Thermal Processing .............................................................527 Takashi Okazaki and Kanichi Suzuki Chapter 18 pH-Assisted Thermal Processing......................................................................567 Alfredo Palop and Antonio Martnez Chapter 19 TimeTemperature Integrators for Thermal Process Evaluation .....................597 Antonio Martnez, D. Rodrigo, P.S. Fernndez, and M. J. Ocio Index .................................................................................................................621 DK3951_C000.fm Page xv Monday, October 24, 2005 11:00 AM DK3951_C000.fm Page xvi Monday, October 24, 2005 11:00 AM Part I Modeling of Thermal Food Processes DK3951_Part_I.fm Page 1 Monday, October 24, 2005 11:55 AM DK3951_Part_I.fm Page 2 Monday, October 24, 2005 11:55 AM 3 1 Thermal Physical Properties of Foods A.E. Delgado, Da-Wen Sun, and A.C. Rubiolo CONTENTS 1.1 Introduction..................................................................................................31.2 Denition and Measurement of Thermophysical Properties......................41.2.1 Specic Heat Capacity ....................................................................51.2.2 Enthalpy...........................................................................................51.2.3 Thermal Conductivity......................................................................61.2.4 Thermal Diffusivity .........................................................................71.2.5 Density.............................................................................................71.2.6 Dielectric Constant and Dielectric Loss Factor..............................81.3 Data Sources on Thermophysical Properties ............................................101.4 Predictive Equations ..................................................................................121.4.1 Specic Heat..................................................................................121.4.1.1 Specic Heat of Juices...................................................151.4.1.2 Specic Heat of Meats...................................................151.4.1.3 Specic Heat of Fruits and Vegetables..........................161.4.1.4 Specic Heat of Miscellaneous Products ......................161.4.2 Enthalpy.........................................................................................171.4.3 Thermal Conductivity and Thermal Diffusivity ...........................171.4.3.1 Thermal Conductivity of Meats.....................................201.4.3.2 Thermal Conductivity and Thermal Diffusivityof Juices, Fruits and Vegetables, and Others.................221.4.4 Density...........................................................................................231.4.5 Dielectric Properties ......................................................................251.5 Conclusions................................................................................................28References ...........................................................................................................30 1.1 INTRODUCTION Thermal food processes, whether electrical or conventional, may be broadlyclassied as unit operations in blanching, cooking, drying, pasteurization, steril-ization, and thawing, and involve raising the product to some nal temperaturethat depends on the particular objective of the process. 1 The design, simulation, DK3951_C001.fm Page 3 Monday, October 24, 2005 11:01 AM 4 Thermal Food Processing: New Technologies and Quality Issues optimization, and control of any of these processes require the knowledge of basicengineering properties of foods.Thermophysical properties in particular are within the more general groupof engineering properties and primarily comprise specic heat and enthalpy,thermal conductivity and diffusivity, and heat penetration coefcient. Other prop-erties of interest are initial freezing point, freezing range, unfreezable watercontent, heat generation (and evaporation), and the more basic physical propertyof density. 2 The thermal properties depend on the chemical composition, structure of theproduct, and temperature; however, the processing of the food and the method ofmeasurement are important as well. The temperature range of interest to foodengineers, 50 to 150 C, covers two areas of food engineering, the applications ofheat and cold. At low temperatures, where the conversion of water into ice takesplace, the change in thermophysical properties is dramatic for all water-rich foods.However, the upper end, which is the temperature range considered here, is lessdramatic. Despite that, products rich in fat will also show phase change effects. 2 In general, for each property, the following information is normally sought:(1) reliable method(s) of measurement, (2) key food component(s), and (3) widelyapplicable predictive relationships. 3 Sensitivity tests have demonstrated the sig-nicance of the thermophysical properties. 4 For example, two thermal properties,thermal conductivity and specic heat, and two mechanical properties, densityand viscosity, determine how a food product heats after microwave energy hasbeen deposited in it. 5 The thermal properties treated in this chapter are specic heat, thermal con-ductivity, thermal diffusivity, and density. Since alternative methods to supplyheat are considered in this book (e.g., radio frequency and microwave heating),the dielectric constant and dielectric loss factor are also taken into account. 1.2 DEFINITION AND MEASUREMENT OF THERMOPHYSICAL PROPERTIES The measurement of the thermal properties has been notably described previouslyby many authors in the literature 611 and will not be detailed here. Thermalproperties of food and their measurement, data availability, calculation, andprediction have also been well described as one of the subjects undertaken withinCOST90, the rst food technology project of COST. 2,1214 Dielectric propertieshave also been discussed within electrical properties in the other EU concertedproject, COST90bis. 15 Therefore, a brief comment on the recommended methodsused to measure thermal properties is given below.For most engineering heat transfer calculations performed in commercial heat-ing or cooling applications, accuracies greater than 2 to 5% are seldom needed,because errors due to variable or inaccurate operating conditions (e.g., air velocity,temperature) would overshadow errors caused by inaccurate thermal properties. 9 Thus, precision and accuracy of measurement with regard to the application of thedata are important factors to consider when selecting a measurement method. DK3951_C001.fm Page 4 Monday, October 24, 2005 11:01 AM Thermal Physical Properties of Foods 5 1.2.1 S PECIFIC H EAT C APACITY The heat capacity ( c ) of a substance is dened as the amount of heat necessaryto increase the temperature of 1 kg of material by 1 C at a given temperature. Itis expressed as Joules per kilogram Kelvin in SI units, and it is a measure of theamount of heat to be removed or introduced in order to change the temperatureof a material. If T is the increase in temperature of a given mass, m , as aconsequence of the application of heat, Q , the calculated specic heat is theaverage, that is:(1.1)If T is small, and q

Q / m , Equation 1.1 gives the instantaneous value of c : 11 . (1.2)If both a temperature change and a thermal transition are included, this specicheat is then called the apparent specic heat.There exist two specic heats, c p and c v ; the former is for constant pressureprocess and the latter for constant volume process. The specic heat for solidsand liquids is temperature dependent, but does not depend on pressure, unlessvery high pressures are applied. For the food industry, c p is commonly used, asmost of the food operations are at atmospheric pressure. Only with gases it isnecessary to distinguish between c p and c v . The methods often used to measure the specic heat and also the enthalpyare the method of mixing, the adiabatic calorimeter, and the differential scanningcalorimeter (DSC). Over the years, Riedel 1619 has published extensively on boththe specic heat and enthalpy of a wide range of food products. 20 He used theadiabatic calorimeter, which is a method that can provide high precision butinvolves long measuring times and difculties for preparing the sample. AlthoughDSC has disadvantages, such as necessity of calibration and requirement of smallsamples and good thermal contact, it is the method generally recommended formeasuring specic heat. 1.2.2 E NTHALPY Enthalpy is the heat content or energy level in a system per unit mass, and theunit is Joules per kilogram (J/kg). It can be written in terms of specic heat as: 10 (1.3)cQm Taveg .cqTdqdTTT T

_,

_,

lim 0H cdT . DK3951_C001.fm Page 5 Monday, October 24, 2005 11:01 AM 6 Thermal Food Processing: New Technologies and Quality Issues The specic heat and enthalpy are properties of state. Enthalpy has beenused more for quantifying energy in steam than in foods. It is also convenientfor frozen foods because it is difcult to separate latent and sensible heats infrozen foods, which often contain some unfrozen water even at very lowtemperatures. 9 1.2.3 T HERMAL C ONDUCTIVITY Thermal conductivity ( k ) represents the basic thermal transport property, and itis a measure of the ability of a material to conduct heat. It is dened by the basictransport equation written as Fouriers law for heat conduction in uids or solids,which is integrated to give:(1.4)where q is the heat transfer rate in Watts (W), A is the cross-sectional area normalto the direction of the heat ow in square meters (m 2 ), z is the thickness of thematerial (in meters [m]), T 1 and T 2 are the two surface temperatures of the material,and k is the thermal conductivity in Watts per meter Kelvin (W/m K). Thermalconductivity is an intrinsic property of the material. For hygroscopic moist porousmaterials, k is a strong function of the porosity of the material. 21 Heat transfer inporous moist materials may occur by heat conduction and mass transfer simul-taneously, so the effective thermal conductivity is used to precisely evaluate thecoupled heat and moisture transfer through porous materials.For measuring the thermal conductivity of foods, the line heat source probehas frequently been used and is the method recommended for most foodapplications. This technique is implemented in two designs: the hot-wire k apparatus and the k probe. The hot-wire apparatus is widely accepted as themost accurate method for measuring the k of liquids and gases, but it is morecomplicated to adapt to instrumentation and more difcult to use in solidmaterials. 22 The k probe method is fast, uses small samples, and requires knownand available instrumentation. 23 However, it is not well suited for nonviscousuids due to convection currents that arise during probe heating. 9 The tech-nique has also been used to measure k of moist porous foods materials atelevated temperatures. 24 Although the thermal conductivity probe is derivedfrom an idealized heat transfer model, there are unavoidable differencesbetween the real probe and the theoretical model, which cause errors in theapplication of the k probe and lead researchers to corrective measures to eithercompensate or minimize these errors. 22 Various design parameters of the k probe have been analyzed and recommendations given for applications tononfrozen food materials. 22 As a result, it is recommended that users shoulddesign their thermal conductivity probes using the highest acceptable error fortheir intended application.qAk T Tz

( ),1 2 DK3951_C001.fm Page 6 Monday, October 24, 2005 11:01 AM Thermal Physical Properties of Foods 7 1.2.4 T HERMAL D IFFUSIVITY Thermal diffusivity ( ) determines how rapidly a heat front moves or diffusesthrough a material and can be dened as(1.5)where r is the density (kg/m 3 ), c p is the specic heat at constant pressure (J/kg K),and k is the thermal conductivity (W/m K) of the material. The SI unit of is square meters per second (m 2 /sec). Thermal diffusivity measures the abilityof a material to conduct thermal energy relative to its ability to store thermalenergy; products of large values will respond quickly to changes in theirthermal environment, while materials of small values will respond moreslowly.The thermal diffusivity of unfrozen foods ranges from about 1.0 10 7 to1.5 10 7 m 2 /sec and does not change substantially with moisture and temperaturebecause any changes of k are compensated by changes of the density of thematerial. 21 In microwave heating, for example, the fact that thermal diffusivitiesof unfrozen foods are similar means that foods heat similarly for equivalent energydeposition. 5 The measurement of thermal diffusivity can be divided into two groups: directmeasurement and indirect prediction . 10 Indirect prediction, that is, the estimationfrom experimentally measured values of thermal conductivity, specic heat, anddensity, is the recommended method to determine . 9 Since specic heat can beestimated with sufcient accuracy from the product composition, the experimentaldeterminations are the thermal conductivity and the mass density. 9 1.2.5 D ENSITY Density ( ) is a physical property widely used in process calculations. Densityof food materials depends on temperature and composition, and it is the unit massper unit volume:(1.6)The SI unit of density is kilograms per cubic meter (kg/m 3 ). Different ways ofdensity denition, measurement, and usage in process calculations are well dis-cussed in the literature. 10 In some cases, the apparent density is used as bulkdensity . The apparent density is the density of a substance, including all poresremaining in the material, while bulk density is the density of a material whenpacked or stacked in bulk. 10 Hence, it is necessary to mention the denition ofdensity when presenting or using data in process calculations. 10

kcp, mVs. DK3951_C001.fm Page 7 Monday, October 24, 2005 11:01 AM 8 Thermal Food Processing: New Technologies and Quality IssuesThe density of a food product is measured by weighing a known volume ofthe product. Since food products are different in shape and size, the accuratemeasurement of volume can be challenging.25 An easy procedure recommendedfor measuring r in meats is to add a known mass (approximately 5 g) of sampleto a calibrated 60-ml ask, and complete the volume with distilled water at 22C.11Density is evaluated from the following equation:(1.7)where m and Vs are the mass and volume of the sample, respectively, calculatedfrom the added water volume Vw.The bulk and solids densities can be measured experimentally, and they canbe used to estimate the bulk porosity. Porosity is an important physical property,since its changes during processing may have signicant effects on the heat andmass transport properties (e.g., thermal conductivity), and thus the quality (nutri-tive and sensory) of the food product.41.2.6 DIELECTRIC CONSTANT AND DIELECTRIC LOSS FACTORElectrical properties of foods are of general interest as they correlate the physicalattributes of foods with their chemical ones, and they are of practical interest inoptimization and control of dielectric heating processes.26 The most intensivelyinvestigated electrical properties of foods have been the relative dielectric con-stant (e) and loss factor (e). These dielectric properties determine the energycoupling and distribution in a material subjected to dielectric heating.27 Thedielectric constant or capacitivity is related to the materials capacitance andits ability to store electrical energy from an electromagnetic eld, and it is aconstant for a material at a given frequency. The dielectric loss is related to amaterials resistance and its ability to dissipate electrical energy from an electro-magnetic eld.1 A material with high values of the dielectric loss factor absorbsenergy at a faster rate than materials with lower loss factors.28 It should alwaysbe remembered that dielectric properties in a time-varying electric eld arecomplex; that is to say, they have two components: real, e, and imaginary, e.29The dielectric loss factor in turn is the sum of two components: ionic, , anddipole, , loss. The ratio of the dielectric loss and dielectric constant is calledthe loss tangent or the dissipation (power) factor of the material (tan d). Thepermitivity, which determines the dielectric constant, the dielectric loss factor,and dielectric loss angle, inuences the dielectric heating.28The relative ionic loss, , is related to the electrical conductivity of a foodmaterial (s) with the following relationship:30(1.8) mVmVs w60, d 20f,DK3951_C001.fm Page 8 Monday, October 24, 2005 11:01 AMThermal Physical Properties of Foods 9where e0 is the permitivity of free space (8.854 1012 F/m), and f is the frequencyof the electromagnetic waves (Hz).Power penetration depth (d), one of the essential dielectric processing param-eters, is dened as the distance that the incident power decreases to 1/e (e 2.718)of its value at the surface.30 The penetration depth is calculated from the dielectricconstant and dielectric loss data by using the following expression:31 (1.9)where c0 is the speed of light in vacuum (3 108 m/sec). An approximation fordetermining the penetration depth that holds for virtually all foods is given by5(1.10)where l0 is the free space microwave wavelength, which can be in any units oflength. For 2450 MHz, l0 is equal to 122 mm. Knowledge of the penetrationdepth helps in selecting a correct sample thickness to guide the microwave orradio frequency (RF) heating processes.30 It has been reported that for mashedpotatoes, for example, after calculating the penetration depth, microwave heatingis advisable for packages with relatively smaller thickness (for example, 10 to20 mm for two-sided heating), and RF heating should be applied for packagesand trays with large institutional sizes (for example, 40 to 80 mm depth).30The food map plot for e vs. with constant penetration depth lines (d) isa recommended way to illustrate the dielectric properties.5The dielectric properties of liquid and semisolid food products depend pri-marily on their moisture, salts, and solids contents. However, the extent to whicheach of these constituents affects food dielectric behavior depends very much onthe processing frequency and the temperature history of the product.1 In anexperiment about the effect of sample heating procedures (temperature beingraised in 10C intervals or being raised directly to a set point, 121C) on theresults of measurements for whey protein gel, cooked macaroni noodles, cheesesauce, and macaroni and cheese, it was found that the heating procedures did notaffect the results of the dielectric property measurements for the materials tested.32Dielectric properties can be measured by the methods reviewed within thecollaborative research project COST90bis.29 The measuring methods can varyeven in a given frequency range. Four groups of measurement methods can beconsidered: lumped circuit, resonator, transmission line, and free space methods.33One of the most commonly used measuring methods employs resonant cavities,since they are very accurate but can also be sensitive to low-loss tangents.28dcf

+

_,

1021 20 11253941 1.tan/ ]]11,,1 2 /,d 02,DK3951_C001.fm Page 9 Monday, October 24, 2005 11:01 AM10 Thermal Food Processing: New Technologies and Quality IssuesThe method can be easily adapted to high (up to 140C) or low (20C)temperatures. Another popular technique is the open-ended coaxial probemethod,28 because it requires no particular sample shapes and offers broad-band measurement.301.3 DATA SOURCES ON THERMOPHYSICAL PROPERTIESThermal property data have been measured since the late 1800s, with almosttwo thirds of that being published in the 1950s and 1960s.9 A problem thatindustrial users normally face is that the data available are often of limitedvalue because information about composition, temperature, error in measure-ment, etc., is not reported. Furthermore, moisture and air content ranges tendto cover a narrow band and thermophysical data at both elevated and lowtemperatures are sparse.34 Though information available is only partial, suchdata are very useful for preliminary design, heat transfer calculations, and foodquality assessment.Different ways can be recognized to obtain information on thermal properties,namely: (1) original publications, (2) summarizing publications such as articles,monographs, and books, (3) bibliographies and compilations of literature refer-ences, (4) handbooks and data books, and nally (5) computerized data banks.2The recommendation of the COST90 project in 1983 was to replace the rst fourchoices mentioned above with one compilation of basic data and thermophysicalproperties by product, containing calculated values and experimental data as refer-ences, accompanied also by a reference to their sources in case more informationwas needed. Computer programs such as COSTHERM and FoodProp were devel-oped for the thermal properties of foods, but the diverse and variable data of otherproperties prevented the development of other computer programs.4 Food PropertiesDatabase, Version 2.0 for Windows,35 was the rst such database assembled in theU.S.34 This database includes over 2400 foodproperty combinations and over 2450food materials; it also features a collection of mathematical models that have beenproposed for predicting food property values. In the EU there is an online databaseavailable for physical properties of agro-food materials (www.nelfood.com).34 Thedatabase contains ve main categories of data: thermal, mechanical (rheologicaland textural), electrical, diffusional, and optical (spectral and color) properties. Thefuture work of NELFOOD database will improve the predictive features of thedatabase. The novelty of the database is that it species both the experimentalmethod and the descriptions of the food, and also provides a score (four-point scale)indicating the quality of the method specication and food denition. This charac-teristic in particular is very helpful when selecting appropriate values or modelsfrom many sources available, since it is not only the data but also the interpretationand application that are equally important.References to important sources of information on thermophysical propertieshave been published in the literature2; Table 1.1 presents additional informationon data recently available. The database of the Food Research Institute of PragueDK3951_C001.fm Page 10 Monday, October 24, 2005 11:01 AMThermal Physical Properties of Foods 11contains more than 16,000 manuscripts, which can be accessed in part throughthe NELFOOD database. Average values and variation ranges of thermal con-ductivity of more than 100 food materials, classied into 11 food categories, werealso compiled.36 More than 95% of these data are in the ranges of 0.03 to 2 W/mKfor thermal conductivity, 0.01 to 65 kg/kg db for moisture content, and 43 to160C for temperature range.Very few thermal diffusivity data are available; however, thermal diffusivitycan be calculated from specic heat, thermal conductivity, and mass density9 ifthey are available, as shown in Equation 1.5.A compilation of dielectric property data has been presented (dielectric constante , dielectric loss , and penetration depth d) for a wide range of fruits, vegetables,meats, and sh for the frequency range of 2000 to 3000 MHz.31 The references foreach set of data and the type of measurement used are provided as well. In somecases, the composition data are from sources other than those from which the datawere taken. The amount of information available on the dielectric properties offoods in the RF range is limited in comparison with data at microwave frequencies.Dielectric properties of selected foods in the RF range 1 to 200 MHz have beenreported recently, along with information related to data sources.28 Except for oneTABLE 1.1Literature on Thermal Physical Properties of FoodsSource InformationNesvadba et al. (2004)34http://www.nelfood.comDatabaseThermal, mechanical, electrical, diffusional, and optical properties; data available in tables and equations as function of temperature, pressure, composition, etc. Nesvadba et al. http://www.vupp.cz/envupp/research.htmDatabasePhysical properties data at the Institute of Food Research, PragueKrokida et al. (2001)36ArticleCompilation of thermal conductivity data with range of material moisture content and temperatureSingh (1995)35DatabaseExperimental values and mathematical models of food properties, along with literature citationsRahman (1995)10Food Properties HandbookChapters 3 to 6TextbookDensity, specic heat, enthalpy, latent heat, thermalconductivity, and thermal diffusivityMeasurement, experimental values, and prediction modelsDatta et al. (1995)31Engineering properties of foodsChapter 9Dielectric property data of fruits, vegetables, meats, and shASHRAE (1993)39Fundamentals HandbookChapter 30Specic heat, thermal diffusivity, and thermal conductivityDK3951_C001.fm Page 11 Monday, October 24, 2005 11:01 AM12 Thermal Food Processing: New Technologies and Quality Issueswork,37 very few studies provide the dielectric properties above 65C.38 Dielectricproperties of whey protein gel, cooked macaroni noodles, cheese sauce, and mac-aroni and cheese, at both microwave and radio frequencies (27, 40, 915, and1800 MHz) over a temperature range of 20 to 121.1C, were recently reported.32It is important to note that the data les for specic heat capacity publishedin ASHRAEs Fundamentals Handbook39 are not experimentally measured values;instead, they are calculated from equations based on water content, which canresult in considerable error for calculations.In summary, considerable data on thermal properties have been published to thepresent, though in many cases the information available is only partial. Therefore,when reporting thermal property data, researchers should provide a detailed andinformative description of the product tested (variety, chemical composition, pretreat-ment, etc.), the experimental procedures (process variables), and the data obtained.91.4 PREDICTIVE EQUATIONSThermal processing was the rst food process to which mathematical modelingwas applied, because of its great importance to the publics health and safety andthe economics of food processing.4 Modeling requires the information of the meanor effective values of the components, together with the representation of thephysical structure.11 Because of the large variety of foods and formulations, it isalmost impossible to experimentally measure the thermal properties for all possibleconditions and compositions. Therefore, the most viable option is to predict thethermophysical properties of foods using mathematical models. However, if moreaccuracy is required, a good solution is the experimental determination.Water as a major component in foods affects safety, stability, quality, andphysical properties of food. Analysis of published data shows that the less waterthere is in the material, the more discrepancies between predicted and measuredvalues that exist.27 It seems that discrepancies arise from the treatment of wholewater in food as bulk water, without taking into account the interactions betweenwater and food components, which must affect thermal properties.Most of the thermal property models are empirical rather than theoretical;that is, they are based on statistical curve tting rather than a theoretical derivationinvolving heat transfer analyses.9 A comprehensive compilation of predictiveequations of thermal physical properties of foods is provided in the litera-ture.1012,40 From the many published equations, some examples of commonlyused correlations are given below.1.4.1 SPECIFIC HEATWater has a high specic heat in comparison to other food components; hence,even small amounts of water in foods affect its specic heat substantially.27 Thesimplest specic heat model for low-fat foods has the following form:27cp a + bxw, (1.11)DK3951_C001.fm Page 12 Monday, October 24, 2005 11:01 AMThermal Physical Properties of Foods 13where a and b are constants that depend on the product and temperature, xw isthe water content in decimals, and cp is in Joules per kilogram degrees Centigrade(J/kg C). Table 1.2 lists the constants a and b, the moisture content, and tem-perature range for a great variety of foods.10It is generally accepted that specic heat obeys the rules of additivity. Thismeans that the specic heat of a product is equal to the sum of the fractionalspecic heats of the main constituents.27 Using the additivity principle, specicheat can be calculated as follows:(1.12)where cpi is the specic heat at a constant pressure of the food component i, andxi is the mass fraction of the ith food component (water, xw; protein, xp; fat, xf;carbohydrate, xc, and ash, xas). The thermal properties of the major food compo-nents as a function of temperature can be found in the literature.41 When the foodcontains a large amount of fat, the specic heat is made up from the contributionof the fat fraction and also from the phase transition of the fat.The specic heat above the initial freezing point can be calculated if the cpof the fat is assumed to be half of the cp of water, and the cp of the solids, whichhave similar specic heats, is assumed to be 0.3 times that of waters cp:20,42cp 4180 (0.5xf + 0.3xs + xw). (1.13)TABLE 1.2Linear Models for Specic Heat of FoodsMaterial a b xw Range T Range (C)Foods 837 3349Fish and meats 1670 2500 Less than 0.25Fruits and vegetables 1670 2500 Higher than 0.25Orange (navel) 1452 2515 0.000.89Lentil 1030 4080 0.020.26 1080Potato 904 3266 Higher than 0.5Potato 1645 1830 0.200.50Milk products Cheese (processed) 1918 2258 0.4250.684 40Dulce de leche 1790 2640 0.280.60 3050Sorghum and cereals 1400 3200 Low waterSorghum 1396 3222 0.000.30Wheat (hard red spring) 1090 4046 0.000.40 0.621.1Soybeans 1637 1927Soy our (defatted) 1748 3363 0.0920.391 130Source: Adapted from Rahman, S., Food Properties Handbook, CRC Press, Boca Raton, FL, 1995,pp. 179390.c c xp pi i

,DK3951_C001.fm Page 13 Monday, October 24, 2005 11:01 AM14 Thermal Food Processing: New Technologies and Quality IssuesEquation 1.13 gives a rough estimate of the specic heat above the freezing pointof the product.An empirical equation for the calculation of cp of some different foods is given as43cp 4187 [xw + ( + 0.001T)(1 xw) exp(43xw2.3)], (1.14)where the temperature T is in degrees Centigrade (C) and the numerical valuesof the coefcients in Equation 1.14 for some foods arebeef 0.385, bbeef 0.08white bread 0.350, bwhite bread 0.09sea sh 0.410, bsea sh 0.12low-fat cheese 0.390, blow-fat cheese 0.10.If detailed composition data are not available, the following simpler modelcan be used:44cp 4190 2300xs 628xs3, (1.15)where xs is the mass fraction of solids, and cp is in Joules per kilogram degreesCentigrade (J/kg C).Gupta45 developed the following correlation to predict the specic heat offoods as a function of moisture content and temperature considering 15 types offoods:10cp 2476.56 + 2356xw 3.79T, (1.16)where T is in Kelvin (K), and cp is in Joules per kilogram Kelvin (J/kg K), andxw ranges from 0.001 to 0.80 and T from 303 to 336 K. Equation 1.16 gives fairlygood values for substances like sugar, wheat our, starch, dry milk, rice, etc. Forsubstances containing higher moisture (more than 80%), Equation 1.16 showshigher deviations from reported values.The specic heat is related to the dielectric properties and the temperatureincrease (T) through the following equation:28(1.17)where t is the temperature rise time (sec), e0 is the dielectric constant of freespace, and V, the electric eld strength, is equal to voltage/distance betweenplates (V/cm). Equation 1.17 shows that the specic heat affects the resulting T.Ttf Vcp

202 tan,DK3951_C001.fm Page 14 Monday, October 24, 2005 11:01 AMThermal Physical Properties of Foods 15A material with greater specic heat will undergo a smaller temperature changesince more energy is required to increase the temperature of 1 g of the materialby 1C.28 In a multicomponent product, where the components have wide dif-ferences in dielectric and thermal properties, it is often necessary to balanceboth sets of properties in order to approach equal heating for each component.It is usually more fruitful to adjust specic heat rather than dielectric propertiesto obtain such a balance.51.4.1.1 Specic Heat of JuicesThe specic heat for fruit juices with water content greater than 50% can becalculated as follows:46cp 1674.7 + 25.12xw. (1.18)The specic heat (J/kg C) of claried apple juice as a function of concen-tration (6 to 75Brix) and temperature (30 to 90C) can be estimated from11,47cp 3384.57 18.1774Bx + 2.3472T. (1.19)Equation 1.19 gives a good t (correlation coefcient R2 0.99) of the experimentaldata in the entire range of concentrations and temperatures under consideration.Alvarado48 developed a general correlation using 140 data for fruit pulps,with moisture content ranging from 0.012 to 0.945 and temperatures from 20 to40C, which is given below:10cp 1560 [exp(0.9446xw)]. (1.20)1.4.1.2 Specic Heat of MeatsSanz et al.40,49 presented a list with experimental values and the most appropriateequations to calculate the specic heat, thermal conductivity, thermal diffusivity,and density of meats and meat products. The following general correlation formeat products for temperatures above the initial freezing point is proposed:cp 1448(1 xw) + 4187xw. (1.21)cp in lamb meat can be estimated with the following expression:50cp 979 + 3175.4xw, (1.22)where xw is the moisture content in percent wet basis, and cp is in J/kg C.AbuDagga and Kolbe51 measured and modeled the apparent specic heat ofsalt-solubilized surimi paste with 74, 78, 80, and 84% moisture content in theDK3951_C001.fm Page 15 Monday, October 24, 2005 11:01 AM16 Thermal Food Processing: New Technologies and Quality Issuestemperature range 25 to 90C. The following linear model was tted to theexperimental data as function of the temperature and moisture content:cp 2330 + 6T + 14.9xw, (1.23)where cp is in Joules per kilogram degrees Centigrade (J/kg C), and the moisturecontent, xw, is in percent wet basis. Equation 1.23 can be considered a workableengineering model in most design circumstances.1.4.1.3 Specic Heat of Fruits and VegetablesThe specic heat (J/kg C) of Golden Delicious apples for the temperature rangefrom 1 to 60C can be estimated with the following correlation:52cp 3360 + 7.5T, (1.24)and for Granny Smith:cp 3400 + 4.9T. (1.25)Hsu et al.53 proposed the following equation to predict cp (J/kg C) for pistachiowith water contents ranging from 5 to 40% on wet basis:11cp 1074 + 27.79xw. (1.26)cp for potatoes (Desiree variety) can be estimated with the following correlation,which was generated from data obtained with DSC measurements, for a temper-ature range from 40 to 70C and moisture content from 0 to 80% on wet basis:54cp 4180(0.406 + 1.46 103T + 0.203xw 2.49 102xw2). (1.27)The main relative percentage deviation of Equation 1.27 is equal to 3.36%, whichindicates a reasonably good t for practical purposes.1.4.1.4 Specic Heat of Miscellaneous ProductsFor milk, the following expression is proposed55 at temperatures above freezing:9cp 4190xw+ [(1370 + 11.3T)(1 xw)], (1.28)where T is in degrees Celsius, and cp is in Joules per kilogram degrees Centigrade(J/kg C).cp (J/kg C) for processed cheese can be estimated from the generalcorrelation56cp 4101 + 1.2T (1673 + 0.27T)xf (2716 1.1T)xns. (1.29)DK3951_C001.fm Page 16 Monday, October 24, 2005 11:01 AMThermal Physical Properties of Foods 17Equation 1.29 is applicable to a temperature range from 40 to 100C, from 0.316to 0.575 mass fraction of solutes, and from 0.135 to 0.405 mass fraction of nonfatsolids, xns.10Christenson et al.57 assumed that the dependence of the specic heat of breadwith moisture follows a mass fraction model:11cp cpwxw +cpdry solid (1 xw), (1.30)where cp of a dry solid is given bycpdry solid 98 + 4.9T. (1.31)T is in Kelvin (K) for 298 to 358 K temperature range, and cp is in J/kg K.1.4.2 ENTHALPYThe enthalpy content is a relative property. For temperatures above the initial freezingpoint, it can be evaluated with the following general expression:12(1.32)which is valid at atmospheric pressure. If the specic heats, cpi, are independentof temperature, then the following equation should be used:(1.33)1.4.3 THERMAL CONDUCTIVITY AND THERMAL DIFFUSIVITYThermal conductivity and thermal diffusivity strongly depend on moisture con-tent, temperature, composition, and structure or physical arrangement of thematerial (e.g., voids, nonhomogeneities). The thermal conductivity of uid foodsis a weak function of their composition, and simple empirical models can be usedfor its estimation. However, to model the thermal conductivity of solid foods,structural models are needed, due to differences in micro- and macrostructure ofthe heterogeneous materials.21,58Porous foods are difcult to model because of the added complexity of the voidspaces. The effective thermal conductivity depends on the heat ow path throughsolids and voids; it may be affected by pore size, pore shape, percent porosity,particle-to-particle resistance, convection within pores, and radiation across pores.9At low moistures, the thermal conductivity and thermal diffusivity of porous foodsH x c dTi piT

0,H T x ci pi

.DK3951_C001.fm Page 17 Monday, October 24, 2005 11:01 AM18 Thermal Food Processing: New Technologies and Quality Issuesare nonlinear functions of the moisture content, due to signicant changes of bulkporosity; at moistures higher than 30%, k increases linearly with the moisturecontent.4 Despite the attempts in developing structural models to predict the thermalconductivity of foods, a generic model does not exist at the moment.36Since theoretical models have a number of limitations for application in foodmaterial, empirical models are popular and widely used for food process designand control, even though they are valid only for a specic product and experi-mental conditions.59Similar to specic heat, most of the models used to calculate the thermalconductivity of foods with high moisture content have the following form:27(1.34)where c1 and c2 are constants. At xw 1, most of the equations converge on thethermal conductivity of water. Predictions agree at high water contents, anddiscrepancies between experimental and predicted values are marked at low watercontents. Table 1.3 lists some simple equations, which only take into account thewater content of the food (xw is in decimal form). Linear models similar toTABLE 1.3Simple Thermal Conductivity Equations for FoodsMaterial Model ReferenceFruits and vegetables 0 < xw < 0.609Tomato paste 0.538 < xw< 0.708, T 30C10Tomato paste0.538 1, the input is excitatory and when w i < 0, it is inhibitory.The net summation, X , of inputs weighted by the synaptic strength w i atconnection i is(4.1)The net value is then mapped through an activation function of neuron output.The activation function used in the model is a threshold function: y

f ( X ) (4.2) FIGURE 4.3 McCulloch and Pitt neural model. (From McCulloch, W.S. and Pitt, W., Bull. Math. Biophys. , 5, 115133, 1943. With permission.)n functioer ansf Trm Su..2xnx1x..Yf X w xiini

1 DK3951_C004.fm Page 111 Monday, October 24, 2005 11:08 AM 112 Thermal Food Processing: New Technologies and Quality Issues (4.3)where is the threshold value.The neuron models used in current neural networks are constructed in a moregeneral way. The input and output signals are not limited to the binary data, andthe activation function can be any continuous function other than the thresholdfunction used in the earlier model. The activation function is typically a monotonicnondecreasing nonlinear function. Some of the often used activation functionsare (where and are constants):Sigmoid function:(4.4)Hyperbolic function:(4.5)Linear threshold:(4.6)Gaussian function:(4.7) 4.3.3 L EARNING R ULES There are primarily two learning methods used for neural networks: supervisedlearning and unsupervised learning. For supervised learning, the training data setconsists of pairs of input and desired output data. The error signal is generatedas difference between the actual output and the desired output, and then used toadjust weights of networks. For unsupervised learning, only input data are fedinto the network, because the desired output is not known, and thus no expliciterror information is given. The supervised learning networks are the most oftenused neural networks for the modeling purpose. Therefore, only learning rulesused in supervised learning networks are discussed.The learning rule is a method to adjust the weight factors based on trial anderror. Many learning rules have been developed to train neural networks. Themain training method is error-correction learning, 1 which uses the data to adjustf xx( ),,

>,10otherwisef xeax( ) =11+f x xe ee ex xx x( ) tanh( ) + f xxx xx( ) / < zq > Fo > Rdh and zq > Fo> Rdh > V, respectively. The studies were later extended to variable retort temperatureprocesses, demonstrating the excellent performance of ANN models.304.5.4 ANN MODEL-BASED MULTIPLE-RAMP VARIABLE RETORT (MRV) TEMPERATURE CONTROL FOR OPTIMIZATIONOF THERMAL PROCESSINGVariable retort temperature (VRT) thermal processing has been recognized as aninnovative method to improve food product quality and save process times. Thekey to designing a VRT thermal process is to choose a reasonable (optimal) VRTprole for a given food product and package being thermally processed. Theselection of optimal retort temperature proles with a multistage ramp functioninvolving multiple variables is complex and difcult to handle by conventionaloptimization methods.33 The study consisted of three parts: (1) developing asso-ciated prediction models using ANN, (2) investigating the sensitivity of VRTparameters to processing results, and (3) searching for the optimal VRT proleusing a hybrid optimization technique coupling ANN with GA.For the rst part, three separate ANN models were developed for predictionsof process time, average quality retention, and surface cook value, respectively,each as a function of ve input variables: ramp time, t, and four step temperatures,T1, T2, T3, and T4. ANN models were trained and tested by two data sets,respectively, which were generated by a computer simulation program of VRTthermal processing. The statistical results of the modeling performance for allANN models had a correlation coefcient of >0.95 and an average relative errorof T3 >T2 > T1 if the PT or Fs was used as the constraint condition, while T4 was lessthan T3 if Qv was used as the constraint condition.4.5.5 ANALYSIS OF CRITICAL CONTROL POINTSIN DEVIANT THERMAL PROCESSESUSING ARTIFICIAL NEURAL NETWORKSThe basic objective of thermal processing is to meet the safety requirements whiletrying to reduce quality degradation to a minimum. Theoretically, it is possibleto design an optimal processing protocol for any food product, but in practice, itis difcult to obtain truly optimal results since considerable deviations exist inprocess parameters. In cases where deviations go beyond a certain critical level,there can be underprocessing or overprocessing. The former indicates that pro-cessed products cannot meet the sterility requirements for safety and consump-tion, while the latter means that quality destruction is more than optimal. There-fore, it is important to identify critical factors, to assess the effect of theirdeviations on the process calculations, and to establish control actions duringthermal processing to avoid process deviations.Thermal processing is a complex system, and standard processes are estab-lished based on achieving a target process lethality (F value) at a critical point,usually the package center. The required process time (PT) for a given productdepends on the retort temperature (RT), product initial temperature (Ti), coolingwater temperature (Tw), and several product-related properties, such as heatingrate index ( fh), heating lag factor ( jh), and cooling lag factor ( jc). It is necessaryto understand and estimate the inuence of these process parameters and thedeviations from their expected values on the required process time. Chen andRamaswamy33 developed ANN models for (1) evaluating the relative order ofimportance of different critical control variables with respect to process calcu-lations, and (2) developing predictive models to compensate for their deviations.The critical variables studied were retort temperature, initial temperature, cool-ing water temperature, heating rate index, heating lag factor, and cooling lagfactor. Their ranges of deviation from a set point were selected as 2 to 2Cfor RT, 5 to 5C for both Tw and Ti, 2 to 2 min for fh, and 0.2 to 0.2 forboth jc and jh. ANN models were developed and used for analysis of differentcritical variables with respect to their importance on the accumulated lethality,process time, cooling time (CT), and total time (TT) under the given processingconditions. By use of ANN models, the relative orders of importance of criticalvariables within the deviation ranges were as follows: for F, RT > fh > jh > Ti Tw> Ti > Ti fh > RT Ti > jc > RT jh; for PT, RT > fh >> jh > Ti > jc > Ti Tw; for CT, jc > Tw > fh; and for TT, RT > fh > jh > jc > Tw > Ti > Ti jc > Ti Tw. The accepted deviation ranges for various input variables under givencontrol ranges were predicted by NN models, one of which is shown in Figure 4.9.DK3951_C004.fm Page 125 Monday, October 24, 2005 11:08 AM126 Thermal Food Processing: New Technologies and Quality IssuesBased on these graphs, it can be easily determined that when the desired Fvalue was set at 6 0.5 min, the maximum acceptable deviation ranges ofdifferent variables were 0.3C for RT; 4C for Ti; 0.1 for jh; 0.8, 1, and1.2 min for fh at fh = 20, 40, and 60 min, respectively; and 0.4 for jc. Neuralnetwork models were also used for analysis of the combination effect of mul-tiple deviations on F, PT, and CT (shown in Figure 4.10). By use of this graph,the maximum changes in F and PT for different deviation combinations couldbe easily determined.4.6 CONCLUSIONSAs conrmed by a variety of applications reported, the modeling capability ofANNs is not a question; they can be used for complex cases with multiplevariables and nonlinear relationships usually too difcult for conventional meth-ods. In food thermal processing, application of ANN is still relatively new toother academic areas. Although a few studies have been reported, as mentionedin this chapter, about ANN for modeling, optimization, and critical control pointsanalysis of thermal processing, most of them are still on the hypothesis level,meaning that these results have not been used for industrial applications. Fur-thermore, the online use of neural networks in the thermal processing area is stillblank. Therefore, there is more room for researchers to make efforts on applicationof neural networks in the thermal processing area.It should be noted that ANNs are not without limitations. First of all, neuralnetworks work like a black box; thus, ANN models cannot give clear internalrelationships between input and output variables as provided by other modelsFIGURE 4.9 Acceptable deviation ranges predicted by ANN models for heating rate index, fh.0123456789-3 -2 -1 0 1 2 3Deviation of fh(min)F(min)20 min 40 min 60 min20 min40 min60 minDK3951_C004.fm Page 126 Monday, October 24, 2005 11:08 AMModeling Food Thermal Processes Using Articial Neural Networks 127based on conventional methods. Therefore, neural networks should be used asa tool for practical purposes rather than theoretical ones, focusing on devel-oping and understanding the intrinsic relationships of various variables. Forthe practical application, the objective of developing ANN models is that theyare to be used for different purposes such as optimization, online control,identication, etc. In order to achieve this goal, neural networks must becombined with other techniques, for instance, fuzzy logic, expert systems, andgenetic algorithms or other search techniques. Therefore, the future trend forapplication of neural networks should be developing hybrid methods by usingneural networks and other techniques that may have more potential for directuse for industrial purposes, instead of staying at the level that only conrmsthe feasibility of ANN modeling, as most current works have done. Second,the training ANN model needs enough data, which is the most important factoraffecting the performance of ANN models. It is impossible to obtain an ANN modelwith a good performance using limited or bad distribution data. Thus, neuralFIGURE 4.10 The comprehensive effects of multiple deviations predicted by ANN models:(a) lethality value, and (b) heating time.(a)2.924.34.9155.17-1.98-2.61-2.89-2.98 -3-4-20246RT, fhRT, fh,jhRT, fh,jh, Ti RT, fh,jh, Ti, jcRT, fh,jh, Tijc, TwTypes of combination of deviationsChanges of F value (min)+ -(b)-5.1-7.3-8.6 -8.5-8.99.58.48.15.69.1-15-10-5051015Changes of process time (min)+ -RT, fhRT, fh,jhRT, fh,jh, Ti RT, fh,jh, Ti, jcRT, fh,jh, Tijc, TwTypes of combination of deviationsDK3951_C004.fm Page 127 Monday, October 24, 2005 11:08 AM128 Thermal Food Processing: New Technologies and Quality Issuesnetworks are only suitable for problems with a large amount of experimentaldata, or those that can generate data using a separate computer simulator. Inaddition, like all other models, trained ANN models can only be used forpredictions within the ranges of the variable being investigated. Otherwise,the precision of prediction results by ANN models might not be guaranteed.NOMENCLATUREVariables CT Cooling time, minD Decimal deduction time, minDq Decimal destruction time for quality, minEn Equivalent unit energy consumption, kJ/kgEr Relative average error, %E Time-specic particle concentration function or total square errorF Accumulated lethality value, min, or cumulative particle concentration functionFs Surface cook value, minF Heating or cooling rate index, minj Heat or cooling lag factorg Final temperature difference between can center and retort, Ch Transfer coefcient, W/(m2C) H Height of the can, mmPT Process time or heating time, minQv Average quality retention for whole can, %R Correlation coefcient or ratio of diameter to height of canRT Retort temperature, CT Temperature, CT1T4 Step temperature for MRV function, CU Overall heat transfer, W/(m2C)V Volume, m3w Weight (neural network)y Output valueSubscriptsc Coolingdi Desired output valuesdh Diameter to heightfp Fluid to particleDK3951_C004.fm Page 128 Monday, October 24, 2005 11:08 AMModeling Food Thermal Processes Using Articial Neural Networks 129REFERENCES1. WS McCulloch, W Pitt. A logical calculus of the ideas immanent in nervousactivity. Bulletin of Mathematical Biophysics 5: 115133, 1943.2. Anon. Neural Computing: A Technology Handbook for Professional II/PLUS andNeuralWorks Explorer. Pittsburgh, PA: NeuralWare, Inc., 1993, pp. 125.3. Anon. Reference Guide: Software Reference for Professional II/PLUS and Neu-ralworks Explorer. Pittsburgh, PA: NeuralWare, Inc., 1993, pp. 2070.4. S Haykin. Neural Networks: A Comprehensive Foundation. New York: MacmillanCollege Publishing Company, 1994, pp. 6580.5. JJ Hopeld, Neural networks and physical systems with emergent collective com-putational abilities. Proceedings of the National Academy of Sciences of the UnitedStates of America 79: 25542558, 1982.6. PS Neelakanta, DFD Groff. Neural Network Modeling: Statistical Mechanics andCybernetic Perspectives. Boca Raton, FL, CRC Press, 1994, pp. 3367.h Heating i Index, or initial j Indexm Microorganism, or mean valuemax Maximum min Minimum o Desired valueq Quality w Cooling water Greek Symbolsa Thermal diffusivity, m2/secq Threshold value (neural network)r Density, kg/m3, or lethality ratio e ErrorAbbreviationsANN Articial neural networkCCP Critical control pointCDT Come-down timeCRT Constant retort temperatureCUT Come-up timeGA Genetic algorithm MRV Multiple-ramp variable RTD Residence time distributionVRT Variable retort temperatureDK3951_C004.fm Page 129 Monday, October 24, 2005 11:08 AM130 Thermal Food Processing: New Technologies and Quality Issues7. MA Hussain, M Shaur-Rahman, CW Ng. Prediction of pores formation (poros-ity) in foods during drying: generic models by the use of hybrid neural network.Journal of Food Engineering 51: 239248, 2002.8. CR Chen, HS Ramaswamy, I Alli. 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SS Sablani, OD Baik, M Marcotte. Neural network prediction of thermal conduc-tivity of bakery products. Journal of Food Engineering 52: 299304, 2002.21. T Morimoto, JDe Baerdemaeker, Y Hashimoto. An intelligent approach for opti-mal control of fruit storage process using neural networks and genetic algorithms.Computers and Electronics in Agriculture 18: 205224, 1997.22. T Moritmoto, W Purwanto, J Suzuki, Y Hashimoto. Optimization of heat treatmentfor fruit during storage using neural networks and genetic algorithms. Computersand Electronics in Agriculture 19: 87101, 1997.23. S Sreekanth, CR Chen, SS Sablani, HS Ramaswamy, SO Prasher. Neural networkassisted experimental designs for food research. Agricultural Sciences, Journal forScientic Research, SQU (Oman) 5: 97106, 2000.24. SS Sablani, HS Ramaswamy, SO Prasher. Neural network applications in thermalprocessing optimization. Journal of Food Processing and Preservation 19:283301, 1995.25. SS Sablani, HS Ramaswamy, S Sreekanth, SO Prasher. Neural network modelingof heat transfer to liquid particle mixtures in cans subjected to end-over-endprocessing. Food Research International 30: 105116, 1997.DK3951_C004.fm Page 130 Monday, October 24, 2005 11:08 AMModeling Food Thermal Processes Using Articial Neural Networks 13126. CR Chen, HS Ramaswamy. Neural computing approach for modeling of residencetime distribution (RTD) of carrot cubes in a vertical scraped surface heat exchanger(SSHE). Food Research International 33: 549556, 2000.27. M Afaghi, HS Ramaswamy, SO Prasher. Thermal process calculations usingarticial neural network models. Food Research International 34: 5565, 2001.28. CR Chen. Application of Computer Simulation and Articial Intelligence Tech-nologies for Modeling and Optimization of Food Thermal Processing. Ph.D.thesis, McGill University, Montreal, Canada, 2001.29. CR Chen, HS Ramaswamy. 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Transactions of IChemE, Part C82: 111, 2004.DK3951_C004.fm Page 131 Monday, October 24, 2005 11:08 AMDK3951_C004.fm Page 132 Monday, October 24, 2005 11:08 AM 133 5 Modeling Thermal Processing Using Computational Fluid Dynamics (CFD) Xiao Dong Chen CONTENTS 5.1 Introduction..............................................................................................1335.2 Basic Thermal Processing Parameters ....................................................1345.2.1 Decimal Reduction Time D ........................................................1345.2.2 Thermal Resistance Constant Z ..................................................1365.2.3 Thermal Death Time F ................................................................1365.2.4 Relationships between Chemical Kinetics and ThermalProcessing Parameters .................................................................1365.3 Fundamental Conservation Equations for CFD......................................1375.3.1 Cartesian Coordinate System......................................................1375.3.2 Cylindrical Coordinate System...................................................1385.4 Boundary and Initial Conditions.............................................................1395.4.1 Velocity Boundary Conditions ....................................................1395.4.2 Thermal Boundary Conditions....................................................1405.4.3 Mass Transfer Boundary Conditions ..........................................1405.5 Solution Methods ....................................................................................1415.6 Worked Examples....................................................................................1425.7 Conclusions..............................................................................................146Acknowledgments .............................................................................................149References .........................................................................................................149 5.1 INTRODUCTION In the food industry, thermal processing is referred to as the processes that heat,hold, and cool a product sequentially, which is required to be free of food-borneillness for a desired period. Pasteurization is a type of thermal processing thatreduces the potential of contamination of a special pathogenic microorganism to DK3951_C005.fm Page 133 Monday, October 24, 2005 11:09 AM 134 Thermal Food Processing: New Technologies and Quality Issues a predesigned extent. The product will still need to be refrigerated; otherwise, itwill not be shelf stable. Sterilization is the process that leads to shelf-stableproducts in cans, soft containers, or bottles. 1 This process usually employs a muchgreater temperature than pasteurization. 5.2 BASIC THERMAL PROCESSING PARAMETERS5.2.1 D ECIMAL R EDUCTION T IME D When you subject a living microorganism population, like Escherichia coli , tothermal processing at a constant temperature ( T ), its population will reduce. Atypical plot of the microbial population over time ( N vs. t ) usually shows anexponential-like trend. A semilog plot of N vs. t may be correlated using a lineart, yielding a straight line with a negative slope ( D ):(5.1) D is called the decimal reduction time .In other words, the microbial population reduction may be expressed as(5.2)Obviously, at different T , D would be different. The higher the temperature,the smaller the D value, and this means that the microorganisms are more vul-nerable in a hotter environment.Some typical values of D are g