FUNDAMENTALS OF

FOOD PROCESS ENGINEERING

Second Ed ition

FUNDAMENTALS OF

FOOD PROCESS ENGINEERING

Second Edition

Romeo T. Toledo

CHAPMAN & HALL New York· London

This edition published in 1994 by Chapman & Hall One Penn Plaza New York, NY 10119

Published in Great Britain by Chapman & Hall 2-6 Boundary Row London SEI 8HN

© 1991 by Van Nostrand Reinhold; transfered to Chapman & Hall, 1993 Softcover reprint of the hardcover 1 st edtion 1991

All rights reserved. No part of this book may be reprinted or reproduced or utilized in any form or by any electronic, mechanical or other means, now known or hereafter invented, including photocopying and recording, or by an information storage or retrieval system, without permission in writing from the publishers.

Library of Congress Cataloging-in-Publication Data

Toledo, Romeo Fundamentals of food process engineering / Romeo T. Toledo.-2nd ed.

p. cm. Includes index.

ISBN-13: 978-1-4615-7054-7 DOl: 10.1007/978-1-4615-7052-3

e-ISBN-13: 978-1-4615-7052-3

1. Food industry and trade. 1. Title TP371.T64 1991

664-dc20

British Library Cataloguing in Publication Data also available.

90-22229 crp

Contents

Preface / xi

1 Review of Mathematical Principles and Applications in Food Processing I 1

Graphing and Fitting Equations to Experimental Data / Roots of Equations / 16 Differential Calculus / 27 Integral Calculus / 36 Problems / 45 Suggested Reading / 50

2 Units and Dimensions I 51

Definition of Terms / 51 Systems of Measurement / 52 The SI System / 53 Conversion of Units / 54 The Dimensional Constant (gJ / 57 Determination of Appropriate SI Units / 58 Dimensional Consistency of Equations / 60 Conversion of Dimensional Equations / 61 Problems / 64 Suggested Reading / 65

3 Material Balances I 66

Basic Principles / 66 Material Balance Problems Involved in Dilution, Concentration, and

Dehydration / 73

v

vi CONTENTS

Blending of Food Ingredients / 82 Multistage Processes / 92 Problems / 104 Suggested Reading / 108

4 Gases and Vapors I 109

Equations of State for Ideal and Real Gases / 109 Thermodynamics / 120 Vapor-Liquid Equilibrium / 126 Problems / 130 Suggested Reading / 131

5 Energy Balances I 132

General Principles / 132 Energy Terms / 133 Heat / 133 Properties of Saturated and Superheated Steam / 144 Heat Balances / 150 Problems / 156 Suggested Reading / 159

6 Flow of Fluids I 160

The Concept of Viscosity / 160 Rheology / 163 Continuous Viscosity Monitoring and Control / 197 Flow of Falling Films / 198 Transportation of Fluids / 204 Problems / 225 Suggested Reading / 231

7 Heat Transfer I 232

Mechanisms of Heat Transfer / 232 Temperature-Measuring Devices / 252 Steady-State Heat Transfer / 256 Local Heat Transfer Coefficients / 268 Unsteady-State Heat Transfer / 281 Problems / 296 Suggested Reading / 300

8 Kinetics of Chemical Reactions in Foods I 302

Theory of Reaction Rates / 302 Types of Reactions / 303 Enzymatic Reactions / 305 Reaction Order / 307 The Reaction Rate Constant / 310 Temperature Dependence of Reaction Rates / 311 Problems / 314 Suggested Reading / 314

9 Thermal Process Calculations I 315

CONTENTS vii

Processes and Systems for Stabilization of Foods for Shelf Stable Storage: Systems Requirements / 315

Microbiological Inactivation Rates at Constant Temperature / 324 Effect of Temperature on Thermal Inactivation of Microorganisms / 336 Sterilization of Continuously Flowing Fluids / 339 Sterilizing Value of Process Expressed as Fo / 348 Thermal Process Calculations for Canned Foods / 349 Broken Heating Curves / 380 Quality Factor Degradation / 390 Problems / 393 Suggested Reading / 397

10 Refrigeration I 398

Mechanical Refrigeration System / 398 The Refrigeration Cycle on the Pressure Enthalpy Diagram for a Given

Refrigerant / 402 Example Problems on the Use of Refrigerant Charts / 405 The Condenser and Evaporator / 412 The Compressor / 416 Refrigeration Load / 417 Commodity Storage Requirements / 425 Controlled Atmosphere,tStorage / 425 Problems / 434 Suggested Reading / 436

11 Evaporation I 437

Single Effect Evaporators / 437 Improving the Economy of Evaporators / 448

viii CONTENTS

Essence Recovery / 454 Problems / 454 Suggested Reading / 455

12 Dehydration I 456

Water Activity / 456 Mass Transfer / 470 Psychrometry / 477 Simultaneous Heat and Mass Transfer in Dehydration / 483 The Stages of Drying / 486 Prediction of Drying Times from Drying Rate Data / 487 Spray Drying / 493 Freeze Drying / 498 Problems / 502 Suggested Reading / 505

13 Physical Separation Processes I 507

Filtration / 507 Sieving / 538 Gravity Separations / 540 Problems / 546 Suggested Reading / 547

14 Extraction I 548

General Principles / 551 Diffusion / 551 Solubility / 552 Equilibrium / 552 Solid Liquid Extraction: Leaching / 552 Supercritical Fluid Extraction / 564 Problems / 566 Suggested Reading / 566

Appendixes I 567

Appendix A-I. Conversion Factors Expressed as a Ratio / 569 Appendix A-2. Properties of Superheated Steam / 571 Appendix A-3. Saturated Steam Tables-English Units / 572 Appendix A-4. Saturated Steam Tables-Metric Units / 574

Appendix A-5. Flow Properties of Food Fluids / 576 Appendix A-6. Psychrometric Chart-English Units / 577 Appendix A-7. Psychrometric Chart-Metric Units / 578

CONTENTS ix

Appendix A-8. BASIC Program for Determination of Thermal Conductivity Above and Below Freezing / 579

Appendix A-9. Thermal Conductivity of Materials of Construction and Insulating Materials / 580

Appendix A-lO. Thermal Conductivity of Foods / 582 Appendix A-II. BASIC Program for Thermophysical Properties of Foods

from Their Composition / 583 Appendix A-I2. Correlation Equations for Heat Transfer Coefficients / 586 Appendix A-l3. BASIC Program for Evaluating Temperature Response of a

Brick-Shaped Solid / 588 Appendix A-I4. BASIC Program for Evaluating Local Heat Transfer

Coefficient from Temperature Response of a Brick-Shaped Solid I 592 Appendix A-I5. Thermal Conductivity of Water as a Function of

Temperature / 594 Appendix A-I6. Density of Water as a Function of Temperature I 595 Appendix A-I7. Viscosity of Water as a Function of Temperature I 596

PREFACE

Ten years after the publication of the first edition of Fundamentals of Food Process Engineering, there have been significant changes in both food science education and the food industry itself. Students now in the food science curric­ulum are generally better prepared mathematically than their counterparts two decades ago. The food science curriculum in most schools in the United States has split into science and business options, with students in the science option following the Institute of Food Technologists' minimum requirements. The minimum requirements include the food engineering course, thus students en­rolled in food engineering are generally better than average, and can be chal­lenged with more rigor in the course material.

The food industry itself has changed. Traditionally, the food industry has been primarily involved in the canning and freezing of agricultural commodi­ties, and a company's operations generally remain within a single commodity. Now, the industry is becoming more diversified, with many companies involved in operations involving more than one type of commodity. A number of for­mulated food products are now made where the commodity connection becomes obscure. The ability to solve problems is a valued asset in a technologist, and often, solving problems involves nothing more than applying principles learned in other areas to the problem at hand. A principle that may have been commonly used with one commodity may also be applied to another commodity to produce unique products. Numerous examples may be cited where processes used in the food industry were adapted from the chemical or textile industries. The food industry is now also involved in sophisticated separation processes, to make higher-value ingredients, remove undesirable components from naturally oc­curring food sources, or to recover valuable components from food processing byproducts. In addition, federal, state, and local regulations for public health, worker safety, and environmental protection require a knowledge not only of making the product, but also of techniques for the elimination of microbial hazards, for packaging, and for the reduction of point discharge of pollutants to the environment. Present and future consumers are quality and safety con-

xi

xii PREFACE

scious, and most are willing to pay for quality, safety, and convenience. In­corporating all of these features into processed food products requires the de­velopment of new processes and optimized processing procedures. The old art in food processing and preservation, and the trial-and-error method of making acceptable products, must be replaced by the scientific method, if a company wants priority in product introduction and to generate a marketing edge. These changes in the food industry mean faster career advancement for those who are better prepared technically, and food engineering brings an extra dimension to the training of a food technologist.

Learning food engineering is different from learning other courses in the food science curriculum. Students have to be warned that memorizing a solution to a problem is not recommended. What matters is learning how to recognize prin­ciples, and how to utilize these principles in formulating a solution to a prob­lem. To be effective in demonstrating this ability of application, rather than rote memorization, practice and test problems must be made different from solved example problems.

These trends in both the food industry and food science education have been taken into consideration in the revision of Fundamentals of Food Process En­gineering. New example problems have been added, the calculus is more lib­erally used in this edition as compared to the first edition, and a number of current developments in the field have been incorporated. A recurring theme in the book is the principle of similitude (i.e., most processes are similar when viewed from the standpoint of mass and energy transport). These show up in the derivation of equations where the same physical principles are generally used as the starting point in the derivation. The description of equipment is included only when it is essential in establishing how parameters for their effi­cient operation are selected. Quantification of the relationships between oper­ating variables, equipment size, and product quality is the primary objective of food process engineering, as presented in this book.

There is often not enough time in a term to teach all of the subjects covered in this edition. Instructors can choose which subjects should be covered in depth. The coverage of subjects of contemporary interest enables students to connect the relevance of the subject matter to their career development. News media articles, trade publications, and announcements of symposia or short courses may be used as a guide in the selection of subjects of contemporary interest.

A review chapter on mathematics is included. This was viewed as a useful feature in the first edition. It is recommended that this chapter not be taught as a review of mathematics, but rather as assigned reading prior to the first use of a mathematical principle in the solution of a problem in later sections of the textbook. BASIC programming is also included. The use of computers is be­coming more common in schools and in the workplace and, in the coming de­cade, most college-bound high school students should be familiar with writing and using computer programs. Again, this may be treated as assigned reading

PREFACE xiii

if computer solutions to some of the examples or end of chapter problems are to be covered in class. The chapter on units and dimensions may be used in the same way, although the author has experienced good results in later chapters when units, conversion, and the assessment of equations for dimensional con­sistency have been thoroughly discussed.

The chapter on thermal processing has been expanded. The subject of ther­mobacteriology is one unique area in food processing where chemistry, micro­biology, and engineering are simultaneously applied in the solution of a pro­cessing problem. With the current emphasis on food safety and product quality, knowing how optimal processes for microbial inactivation are determined is a must for every food technologist. To complement the expansion of the thermal processing chapter, a section on unsteady state heat transfer has been added in the chapter on heat transfer.

The author has been careful, in the preparation of the manuscript for this edition, to eliminate errors. Students and colleagues have been very helpful in catching errors. Special thanks is due to Dr. Richard Hartel for an extremely helpful review. If some errors remain when the book is printed, responsibility for those rests solely on the author.

Romeo T. Toledo

FUNDAMENTALS OF

FOOD PROCESS ENGINEERING

Second Edition