Latif M. Jiji. Heat Convection. With 206 Figures and 16 Tables

Transcription

1 Heat Convection

2 Latif M. Jiji Heat Convection With 206 Figures and 16 Tables

3 Prof. Latif M. Jiji City University of New York School of Engineering Dept. of Mechanical Engineering Convent Avenue at 138th Street New York, NY USA Library of Congress Control Number: ISBN Springer Berlin Heidelberg New York ISBN Springer Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. Springer is a part of Springer Science + Business Media springer.com Springer-Verlag Berlin Heidelberg 2006 Printed in The Netherlands The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover Design: Erich Kirchner, Heidelberg Cover Image: Microchannel convection, courtesy of Fluent Inc. Production: SPI Publisher Services, Pondicherry Printed on acid free paper 30/3100/as

4 To my sister Sophie and brother Fouad for their enduring love and affection

5 PREFACE Why have I chosen to write a book on convection heat transfer when several already exist? Although I appreciate the available publications, in recent years I have not used a text book to teach our graduate course in convection. Instead, I have relied on my own notes, not because existing textbooks are unsatisfactory, but because I preferred to select and organize the subject matter to cover the most basic and essential topics and to strike a balance between physical description and mathematical requirements. As I developed my material, I began to distribute lecture notes to students, abandon blackboard use, and rely instead on PowerPoint presentations. I found that PowerPoint lecturing works most effectively when the presented material follows a textbook very closely, thus eliminating the need for students to take notes. Time saved by this format is used to raise questions, engage students, and gauge their comprehension of the subject. This book evolved out of my success with this approach. This book is designed to: Provide students with the fundamentals and tools needed to model, analyze, and solve a wide range of engineering applications involving convection heat transfer. Present a comprehensive introduction to the important new topic of convection in microchannels. Present textbook material in an efficient and concise manner to be covered in its entirety in a one semester graduate course. Liberate students from the task of copying material from the blackboard and free the instructor from the need to prepare extensive notes. Drill students in a systematic problem solving methodology with emphasis on thought process, logic, reasoning, and verification. Take advantage of internet technology to teach the course online by posting ancillary teaching materials and solutions to assigned problems.

6 viii Hard as it is to leave out any of the topics usually covered in classic texts, cuts have been made so that the remaining materials can be taught in one semester. To illustrate the application of principles and the construction of solutions, examples have been carefully selected, and the approach to solutions follows an orderly method used throughout. To provide consistency in the logic leading to solutions, I have prepared all solutions myself. This book owes a great deal to published literature on heat transfer. As I developed my notes, I used examples and problems taken from published work on the subject. As I did not always record references in my early years of teaching, I have tried to eliminate any that I knew were not my own. I would like to express regret if a few have been unintentionally included. Latif M. Jiji New York, New York January 2006

7 CONTENTS Preface vii CHAPTER 1: BASIC CONCEPTS Convection Heat Transfer Important Factors in Convection Heat Transfer Focal Point in Convection Heat Transfer The Continuum and Thermodynamic Equilibrium Concepts Fourier s Law of Conduction Newton s Law of Cooling The Heat Transfer Coefficient h Radiation: Stefan-Boltzmann Law Differential Formulation of Basic Laws Mathematical Background Units Problem Solving Format 13 REFERENCES 17 PROBLEMS 18 CHAPTER 2: DIFFERENTIAL FORMULATION OF THE BASIC LAWS Introduction Flow Generation Laminar vs. Turbulent Flow Conservation of Mass: The Continuity Equation 22

8 x Contents Cartesian Coordinates Cylindrical Coordinates Spherical Coordinates Conservation of Momentum: The Navier-Stokes Equations of Motion Cartesian Coordinates Cylindrical Coordinates Spherical Coordinates Conservation of Energy: The Energy Equation Formulation: Cartesian Coordinates Simplified form of the Energy Equation Cylindrical Coordinates Spherical Coordinates Solution to the Temperature Distribution The Boussinesq Approximation Boundary Conditions Non-dimensional Form of the Governing Equations: Dynamic and Thermal Similarity Parameters Dimensionless Variables Dimensionless Form of Continuity Dimensionless Form of the Navier-Stokes Equations of 53 Motion Dimensionless Form of the Energy Equation Significance of the Governing Parameters Heat Transfer Coefficient: The Nusselt Number Scale Analysis 59 REFERENCES 61 PROBLEMS 62 CHAPTER 3: EXACT ONE-DIMENSIONAL SOLUTIONS Introduction Simplification of the Governing Equations Exact Solutions Couette Flow Poiseuille Flow Rotating Flow 86 REFERENCES 93 PROBLEMS 94

9 Contents xi CHAPTER 4: BOUNDARY LAYER FLOW: APPLICATION TO EXTERNAL FLOW Introduction The Boundary Layer Concept: Simplification of the 99 Governing Equations Qualitative Description The Governing Equations Mathematical Simplification Simplification of the Momentum Equations Simplification of the Energy Equation Summary of Boundary Layer Equations for Steady Laminar 114 Flow 4.4 Solutions: External Flow Laminar Boundary Layer Flow over Semi-infinite Flat Plate: Uniform Surface Temperature Applications: Blasius Solution, Pohlhausen s Solution, and Scaling Laminar Boundary Layer Flow over Semi-infinite Flat Plate: Variable Surface Temperature Laminar Boundary Layer Flow over a Wedge: Uniform Surface Temperature 143 REFERENCES 149 PROBLEMS 150 CHAPTER 5: APPROXIMATE SOLUTIONS: THE INTEGRAL METHOD Introduction Differential vs. Integral Formulation Integral Method Approximation: Mathematical Simplification Procedure Accuracy of the Integral Method Integral Formulation of the Basic Laws Conservation of Mass Conservation of Momentum Conservation of Energy Integral Solutions Flow Field Solution: Uniform Flow over a Semi-infinite Plate Temperature Solution and Nusselt Number: Flow over a Semi-infinite Plate 173

10 xii Contents Uniform Surface Flux 185 REFERENCES 193 PROBLEMS 194 CHAPTER 6: HEAT TRANSFER IN CHANNEL FLOW Introduction Hydrodynamic and Thermal Regions: General Features Flow Field Temperature Field Hydrodynamic and Thermal Entrance Lengths Scale Analysis Analytic and Numerical Solutions: Laminar Flow Channels with Uniform Surface Heat Flux Channels with Uniform Surface Temperature Determination of Heat Transfer Coefficient h(x) and Nusselt Number Nu D Scale Analysis Basic Considerations for the Analytical Determination of Heat Flux, Heat Transfer Coefficient and Nusselt Number Heat Transfer Coefficient in the Fully Developed Temperature Region Definition of Fully Developed Temperature Profile Heat Transfer Coefficient and Nusselt Number Fully Developed Region for Tubes at Uniform Surface Flux Fully Developed Region for Tubes at Uniform Surface Temperature Nusselt Number for Laminar Fully Developed Velocity and Temperature in Channels of Various Cross-Sections Thermal Entrance Region: Laminar Flow Through Tubes Uniform Surface Temperature: Graetz Solution Uniform Surface Heat Flux 252 REFERENCES 254 PROBLEMS 255 CHAPTER 7: FREE CONVECTION Introduction 259

11 Contents xiii 7.2 Features and Parameters of Free Convection Governing Equations Boundary Conditions Laminar Free Convection over a Vertical Plate: Uniform Surface Temperature Assumptions Governing Equations Boundary Conditions Similarity Transformation Solution Heat Transfer Coefficient and Nusselt Number Laminar Free Convection over a Vertical Plate: Uniform Surface Heat Flux Inclined Plates Integral Method Integral Formulation of Conservation of Momentum Integral Formulation of Conservation of Energy Integral Solution Comparison with Exact Solution for Nusselt Number 288 REFERENCES 289 PROBLEMS 290 CHAPTER 8: CORRELATION EQUATIONS: FORCED AND FREE CONVECTION Introduction Experimental Determination of Heat Transfer Coefficient h Limitations and Accuracy of Correlation Equations Procedure for Selecting and Applying Correlation Equations External Forced Convection Correlations Uniform Flow over a Flat Plate: Transition to Turbulent Flow External Flow Normal to a Cylinder External Flow over a Sphere Internal Forced Convection Correlations Entrance Region: Laminar Flow Through Tubes at Uniform Surface Temperature Fully Developed Velocity and Temperature in Tubes: Turbulent Flow Non-circular Channels: Turbulent Flow Free Convection Correlations External Free Convection Correlations Free Convection in Enclosures 319

12 x iv Contents 8.8 Other Correlations 328 REFERENCES 329 PROBLEMS 331 CHAPTER 9: CONVECTION IN MICROCHANNELS Introduction Continuum and Thermodynamic Hypothesis Surface Forces Chapter Scope Basic Considerations Mean Free Path Why Microchannels? Classification Macro and Microchannels Gases vs. Liquids General Features Flow Rate Friction Factor Transition to Turbulent Flow Nusselt number Governing Equations Compressibility Axial Conduction Dissipation Velocity Slip and Temperature Jump Boundary Conditions Analytic Solutions: Slip Flow Assumptions Couette Flow with Viscous Dissipation: Parallel Plates with Surface Convection Fully Developed Poiseuille Channel Flow: Uniform Surface Flux Fully Developed Poiseuille Channel Flow: Uniform Surface Temperature Fully Developed Poiseuille Flow in Microtubes: Uniform Surface Flux Fully Developed Poiseuille Flow in Microtubes: Uniform Surface Temperature 402 REFERENCES 404 PROBLEMS 406

13 Contents xv APPENDIX A Conservation of Energy: The Energy Equation 413 APPENDIX B Pohlhausen s Solution 422 APPENDIX C Laminar Boundary Layer Flow over Semiinfinite Plate: Variable Surface Temperature 426 APEENDIC D Properties of Dry Air at Atmospheric Pressure 429 APPENDIX E Properties of Saturated Water 430 INDEX 431