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Series in Computational and Physical Processes in Mechanics and Thermal Sciences (Formerly the Series in Computational Methods in Mechanics and Thermal Sciences)

W. J. Minkowycz and E. M. Sparrow, Editors
Anderson, Tannehill, and Pletcher, Computational Fluid Mechanics and Heat Transfer Aziz and Na, Perturbation Methods in Heat Transfer Baker, Finite Element Computational Fluid MechanicsBeck, Cole, Haji-Shiekh, and Litkouhi, Heat Conduction Using Green's Functions Chung, Editor, Numerical Modeling in Combustion Jaluria and Torrance, Computational Heat Transfer Patankar, Numerical Heat Transfer and Fluid Flow Pepper and Heinrich, The Finite Element Method: Basic Concepts and Applications Shih, Numerical Heat Transfer

NUMERICAL HEAT TRANSFER AND FLUID FLOW

Suhas V. PatankarProfessor of Mechanical Engineering University of Minnesota

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PROCEEDINGS
Chung, Editor, Finite Elements in Fluids: Volume 8 Haji-Sheikh, Editor, Integral Methods in Science and Engineering-90 Shih, Editor, Numerical Properties and Methodologies in Heat Transfer: Proceedings of the Second National Symposium

FORTHCOMING TITLES
Pepper and Heinrich, The Finite Element Method: AdvancedConcepts Pletcher, Anderson, and Tannehill, Computational Fluid Mechanics and Heat Transfer, Second Edition Willmott, Modeling and Dynamics of Regenerative Heat Transfer

To my wife Rajani

NUMERICAL HEAT TRANSFER AND FLUID FWW Copyright © 1980 by Hemisphere Publishing Corporation. All rights reserved. Printed in the United States of America. No part of this publication may be reproduced, stored ina retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. 141516 BCBC 98765

Ubruy of Congre.. Cataloging in Publication Data

Pa tankar, S V Numerical heat transfer and fluid flow. (Series in computational methods in mechanics and thermal sciences) Bibliography: p.Includes index. 1. Heat -Transmission. 2. Fluid dynamics. 3. Numerical analysis. I. Title. II. Series. 536'.2 79-28286 QC320.P37 ISBN 0-89116-522-3 This book was set in Press Roman by Hemisphere Publishing Corporation. The editors were Mary A. Phillips and Edward M. Millman; the production supervisor was Rehekah McKinney; and the typesetter was Sandra F. Watts. BookCrafters, Inc., was printer andbinder.

CONTENTS

Preface 1 INTRODUCTION
1.1 Scope of the Book 1.2 Methods of Prediction 1.2-1 Experimental Investigation 1.2-2 Theoretical Calculation 1.2-3 Advantages of a Theoretical Calculation 1.2-4 Disadvantages of a Theoretical Calculation 1.2-5 Choice of Prediction Method 1.3 Outline of the Book

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1 3 3 3 4 5 7 7

2

MATHEMATICAL DESCRIPTION OF PHYSICAL PHENOMENA
2.1Governing Differential Equations 2.1-1 Meaning of a Differential Equation 2.1-2 Conservation of a Chemical Species 2.1-3 The Energy Equation 2.1-4 A Momentum Equation 2.1-5 The Time-Averaged Equations for Turbulent Flow 2.1-6 The Turbulence-Kinetic-Energy Equation 2.1-7 The General Differential Equation 2.2 Nature of Coordinates 2.2-1 Independent Variables 2.2-2 Proper Choice of Coordinates 2.2-3 One-Wayand Two-Way Coordinates Problems

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CONTENTS CONTENTS

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3 DISCRETIZATION METHODS
3.1 The Nature of Numerical Methods 3.1-1 The Task 3.1-2 The Discretization Concept 3.1-3 The Structure of the Discretization Equation 3.2 Methods of Deriving the Discretization Equations 3.2-1 Taylor-Series Formulation 3.2-2 VariationalFormulation 3.2-3 Method of Weighted Residuals 3.2-4 Control-Volume Formulation 3.3 An Illustrative Example 3.4 The Four Basic Rules 3.5 Closure Problems

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4 HEAT CONDUCTION
4.1 Objectives of the Chapter 4.2 Steady One-dimensio'nal Conduction 4.2-1 The Basic...
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