Solving Problems in Food Engineering

Solving Problems in Food Engineering

Stavros Yanniotis, Ph.D. Author Solving Problems in Food Engineering

Stavros Yanniotis, Ph.D. Department of Food Science and Technology Agricultural University of Athens Athens, Greece ISBN: 978-0-387-73513-9 eisbn: 978-0-387-73514-6 Library of Congress Control Number: 2007939831 # 2008 Springer Science+Business Media, LLC All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC., 233 Spring Street, New York, NY10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper 9 8 7 6 5 4 3 2 1 springer.com

Tell me and I will listen, Show me and I will understand Involve me and I will learn Ancient Chinese Proverb

Preface Food engineering is usually a difficult discipline for food science students because they are more used to qualitative rather than to quantitative descriptions of food processing operations. Food engineering requires understanding of the basic principles of fluid flow, heat transfer, and mass transfer phenomena and application of these principles to unit operations which are frequently used in food processing, e.g., evaporation, drying, thermal processing, cooling and freezing, etc. The most difficult part of a course in food engineering is often considered the solution of problems. This book is intended to be a step-by-step workbook that will help the students to practice solving food engineering problems. It presumes that the students have already studied the theory of each subject from their textbook. The book deals with problems in fluid flow, heat transfer, mass transfer, and the most common unit operations that find applications in food processing, i.e., thermal processing, cooling and freezing, evaporation, psychometrics, and drying. The book includes 1) theoretical questions in the form true or false which will help the students quickly review the subject that follows (the answers to these questions are given in the Appendix); 2) solved problems; 3) semisolved problems; and 4) problems solved using a computer. With the semisolved problems the students are guided through the solution. The main steps are given, but the students will have to fill in the blank points. With this technique, food science students can practice on and solve relatively difficult food engineering problems. Some of the problems are elementary, but problems of increasing difficulty follow, so that the book will be useful to food science students and even to food engineering students. A CD is supplied with the book which contains solutions of problems that require the use of a computer, e.g., transient heat and mass transfer problems, simulation of a multiple effect evaporator, freezing of a 2-D solid, drying, and others. The objectives for including solved computer problems are 1) to give the students the opportunity to run such programs and see the effect of operating and design variables on the process; and 2) to encourage the students to use computers to solve food engineering problems. Since all the programs in this CD are open code programs, the students can see all the equations and the logic behind the calculations. They are encouraged to see how the programs work vii

viii Preface and try to write their own programs for similar problems. Since food science students feel more comfortable with spreadsheet programs than with programming languages, which engineering students are more familiar with, all the problems that need a computer have EXCEL 1 spreadsheet solutions. I introduce the idea of a digital SWITCH to start and stop the programs when the problem is solved by iteration. With the digital SWITCH, we can stop and restart each program at will. When the SWITCH is turned off the program is not running, so that we can change the values of the input variables. Every time we restart the program by turning the SWITCH on, all calculations start from the beginning. Thus it is easy to change the initial values of the input variables and study the effect of processing and design parameters. In the effort to make things as simple as possible, some of the spreadsheet programs may not operate on some sets of parameters. In such cases, it may be necessary to restart the program with a different set of parameters. I am grateful to Dr H. Schwartzberg, who read the manuscripts and made helpful suggestions. I will also be grateful to readers who may have useful suggestions, or who point out errors or omissions which obviously have slipped from my attention at this point. Athens May 2007 Stavros Yanniotis

Contents Preface... vii 1. Conversion of Units... 1 2. Use of Steam Tables... 5 3. Mass Balance... 11 4. Energy Balance... 21 5. Fluid Flow... 33 6. Pumps.... 41 ix

x Contents 7. Heat Transfer By Conduction.... 55 8. Heat Transfer By Convection... 67 9. Heat Transfer By Radiation... 95 10. Unsteady State Heat Transfer... 101 11. Mass Transfer By Diffusion... 141 12. Mass Transfer By Convection... 155 13. Unsteady State Mass Transfer... 163 14. Pasteurization and Sterilization... 181

Contents xi 15. Cooling and Freezing... 193 16. Evaporation... 215 17. Psychrometrics... 237 18. Drying... 253 References................................................. 273 Appendix: Answers to......................... 275 Moody diagram......................................... 280 Gurney-Lurie charts..................................... 281 Heisler charts........................................... 284 Pressure-Enthalpy chart for HFC 134a....................... 285 Pressure-Enthalpy chart for HFC 404a....................... 286 Psychrometric chart...................................... 287 Bessel functions......................................... 288 Roots of d tand=bi... 290 Roots of dj1(d)-bi Jo(d)=0... 291 Roots of d cotd=1-bi.................................... 292 Error function.......................................... 293 Index...................................................... 295