Convective Heat Transfer E-Book

Michel Favre-Marinet

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 360

Veröffentlichungsjahr: 2013

Beschreibung

Convection heat transfer is an important topic both for industrial applications and fundamental aspects. It combines the complexity of the flow dynamics and of the active or passive scalar transport process. It is part of many university courses such as Mechanical, Aeronautical, Chemical and Biomechanical Engineering. The literature on convective heat transfer is large, but the present manuscript differs in many aspects from the existing ones, particularly from the pedagogical point of view. Each chapter begins with a brief yet complete presentation of the related topic. This is followed by a series of solved problems. The latter are scrupulously detailed and complete the synthetic presentation given at the beginning of each chapter. There are about 50 solved problems, which are mostly original with gradual degree of complexity including those related to recent findings in convective heat transfer phenomena. Each problem is associated with clear indications to help the reader to handle independently the solution. The book contains nine chapters including laminar external and internal flows, convective heat transfer in laminar wake flows, natural convection in confined and no-confined laminar flows, turbulent internal flows, turbulent boundary layers, and free shear flows.

Leseprobe

Table of Contents

Foreword

Preface

Chapter 1. Fundamental Equations, Dimensionless Numbers

1.1. Fundamental equations

1.2. Dimensionless numbers

1.3. Flows with variable physical properties: heat transfer in a laminar Couette9 flow

1.4. Flows with dissipation

1.5. Cooling of a sphere by a gas flow

Chapter 2. Laminar Fully Developed Forced Convection in Ducts

2.1. Hydrodynamics

2.2. Heat transfer

2.3. Heat transfer in a parallel-plate channel with uniform wall heat flux

2.4. Flow in a plane channel insulated on one side and heated at uniform temperature on the opposite side

Chapter 3. Forced Convection in Boundary Layer Flows

3.1. Hydrodynamics

3.2. Heat transfer

3.3. Integral method

3.4. Heated jet nozzle

3.5. Asymptotic behavior of thermal boundary layers

3.6. Protection of a wall by a film of insulating material

3.7. Cooling of a moving sheet

3.8. Heat transfer near a rotating disk

3.9. Thermal loss in a duct

3.10. Temperature profile for heat transfer with blowing

Chapter 4. Forced Convection Around Obstacles

4.1. Description of the flow

4.2. Local heat-transfer coefficient for a circular cylinder

4.3. Average heat-transfer coefficient for a circular cylinder

4.4. Other obstacles

4.5. Heat transfer for a rectangular plate in cross-flow

4.6. Heat transfer in a stagnation plane flow. Uniform temperature heating

4.7. Heat transfer in a stagnation plane flow. Step-wise heating at uniform flux

4.8. Temperature measurements by cold-wire

Chapter 5. External Natural Convection

5.1. Introduction

5.2. Boussinesq model1

5.3. Dimensionless numbers. Scale analysis

5.4. Natural convection near a vertical wall

5.5. Integral method for natural convection

5.6. Correlations for external natural convection

5.7. Mixed convection

5.8. Natural convection around a sphere

5.9. Heated jet nozzle

5.10. Shear stress on a vertical wall heated at uniform temperature

5.11. Unsteady natural convection

5.12. Axisymmetric laminar plume

5.13. Heat transfer through a glass pane

5.14. Mixed convection near a vertical wall with suction

Chapter 6. Internal Natural Convection

6.1. Introduction

6.2. Scale analysis

6.3. Fully developed regime in a vertical duct heated at constant temperature

6.4. Enclosure with vertical walls heated at constant temperature

6.5. Thermal insulation by a double-pane window

6.6. Natural convection in an enclosure filled with a heat generating fluid

6.7. One-dimensional mixed convection in a cavity

Chapter 7. Turbulent Convection in Internal Wall Flows

7.1. Introduction

7.2. Hydrodynamic stability and origin of the turbulence

7.3. Reynolds averaged Navier-Stokes equations

7.4. Wall turbulence scaling

7.5. Eddy viscosity-based one point closures

7.6. Some illustrations through direct numerical simulations

7.7. Empirical correlations

7.8. Exact relations for a fully developed turbulent channel flow.

7.9. Mixing length closures and the temperature distribution in the inner and outer layers.

7.10. Temperature distribution in the outer layer

7.11. Transport equations and reformulation of the logarithmic layer

7.12. Near-wall asymptotic behavior of the temperature and turbulent fluxes

7.13. Asymmetric heating of a turbulent channel flow

7.14. Natural convection in a vertical channel in turbulent regime .

Chapter 8. Turbulent Convection in External Wall Flows

8.1. Introduction

8.2. Transition to turbulence in a flat plate boundary layer

8.3. Equations governing turbulent boundary layers

8.4. Scales in a turbulent boundary layer

8.5. Velocity and temperature distributions

8.6. Integral equations

8.7. Analogies

8.8. Temperature measurements in a turbulent boundary layer

8.9. Integral formulation of boundary layers over an isothermal flat plate with zero pressure gradient

8.10. Prandtl-Taylor analogy

8.11. Turbulent boundary layer with uniform suction at the wall

8.12. Turbulent boundary layers with pressure gradient Turbulent Falkner-Skan flows

8.13. Internal sublayer in turbulent boundary layers subject to adverse pressure gradient

8.14. Roughness

Chapter 9. Turbulent Convection in Free Shear Flows

9.1. Introduction

9.2. General approach of free turbulent shear layers

9.3. Plumes

9.4. Two-dimensional turbulent jet.

9.5. Mixing layer

9.6. Determination of the turbulent Prandtl number in a plane wake

9.7. Regulation of temperature

List of symbols

References

Index

First published in France in 2008 by Hermes Science/Lavoisier entitled: Écoulements avec échanges de chaleur volumes 1 et 2 © LAVOISIER, 2008 First published in Great Britain and the United States in 2009 by ISTE Ltd and John Wiley & Sons, Inc.

Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:

ISTE Ltd 27-37 St George’s Road London SW19 4EU UK

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John Wiley & Sons, Inc. 111 River Street Hoboken, NJ 07030 USA

www.wiley.com

© ISTE Ltd, 2009

The rights of Michel Favre-Marinet and Sedat Tardu to be identified as the authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988.

Library of Congress Cataloging-in-Publication Data

Favre-Marinet, Michel, 1947-  [Ecoulements avec échanges de chaleur. English]   Convective heat transfer : solved problems / Michel Favre-Marinet, Sedat Tardu.       p. cm.   Includes bibliographical references and index.   ISBN 978-1-84821-119-3   1. Heat--Convection. 2. Heat--Transmission. I. Tardu, Sedat, 1959- II. Title.    TJ260.F3413 2009    621.402'25--dc22

2009016463

British Library Cataloguing-in-Publication Data A CIP record for this book is available from the British Library ISBN: 978-1-84821-119-3

Foreword

It is a real surprise and pleasure to read this “brainy” book about convective heat transfer. It is a surprise because there are several books already on this subject, and because the book title is deceiving: here “solved problems” means the structure of the field and the method of teaching the discipline, not a random collection of homework problems. It is a pleasure because it is no-nonsense and clear, with the ideas placed naked on the table, as in elementary geometry.

The field of convection has evolved as a sequence of solved problems. The first were the most fundamental and the simplest, and they bear the names of Prandtl, Nusselt, Reynolds and their contemporaries. As the field grew, the problems became more applied (i.e. good for this, but not for that), more complicated, and much more numerous and forgettable. Hidden in this stream, there are still a few fundamental problems that emerge, yet they are obscured by the large volume.

It is here that this book makes its greatest contribution: the principles and the most fundamental problems come first. They are identified, stated and solved.

The book teaches not only structure but also technique. The structure of the field is drawn with very sharp lines: external versus internal convection, forced versus natural convection, rotation, combined convection and conduction, etc. The best technique is to start with the simplest problem solving method (scale analysis) and to teach progressively more laborious and exact methods (integral method, self-similarity, asymptotic behavior).

Scale analysis is offered the front seat in the discussion with the student. This is a powerful feature of the book because it teaches the student how to determine (usually on the back of an envelope) the proper orders of magnitude of all the physical features (temperature, fluid velocity, boundary layer thickness, heat flux) and the correct dimensionless groups, which are the fewest such numbers. With them, the book teaches how to correlate in the most compact form the results obtained analytically, numerically and experimentally.

In summary, this book is a real gem (it even looks good!). I recommend it to everybody who wants to learn convection. Although the authors wrote it for courses at the MS level, I recommend it to all levels, including my colleagues who teach convection.

Adrian BEJANJ. A. Jones Distinguished Professor Duke University Durham, North Carolina April 2009

Preface

Heat transfer is associated with flows in a wide spectrum of industrial and geophysical domains. These flows play an important role in the problems of energy and environment which represent major challenges for our society in the 21st century. Many examples may be found in energy-producing plants (nuclear power plants, thermal power stations, solar energy, etc.), in energy distribution systems (heat networks in towns, environmental buildings, etc.) and in environmental problems, such as waste-heat release into rivers or into the atmosphere. Additionally, many industrial processes use fluids for heating or cooling components of the system (heat exchangers, electric components cooling, for example). In sum, there are a wide variety of situations where fluid mechanics is associated with heat transfer in the physical phenomena or in the processes involved in industrial or environmental problems. It is also worth noting that the devices implied in the field of heat transfer have dimensions bounded by several meters, as in heat exchangers up to tenths of microns in micro heat-transfer applications which currently offer very promising perspectives.

Controlling fluid flows with heat transfer is essential for designing and optimizing efficient systems and requires a good understanding of the phenomena and their modeling. The purpose of this book is to introduce the problems of convective heat transfer to readers who are not familiar with this topic. A good knowledge of fluid mechanics is clearly essential for the study of convective heat transfer. In fact, determining the flow field is most often the first step before solving the associated heat transfer problem. From this perspective, we first recommend consulting some fluid mechanics textbooks in order to get a deeper insight into this subject. Therefore, we recommend the following references (the list of which is not exhaustive):

– general knowledge of fluid mechanics [GUY 91], [WHI 91] [CHA 00] and, in particular, of boundary layer flows [SCH 79];

– turbulent flows [TEN 72], [REY 74], [HIN 75].

The knowledge of conductive heat transfer is, obviously, the second necessary ingredient for studying convective transfer. Concerning this topic, we refer the reader to the following textbooks: [ECK 72], [TAI 95], [INC 96], [BIA 04].

The intention of this book is to briefly introduce the general principles of theory at the beginning of each chapter and then to propose a series of exercises or problems relating to the topics of the chapter. The summary presented at the beginning of each chapter will usefully be supplemented by reading textbooks on convective heat transfer, such as: [BUR 83], [CEB 88], [BEJ 95].

Each problem includes a presentation of the studied case and suggests an approach to solving it. We also present a solution to the problem. Some exercises in this book are purely applications of classical correlations to simple problems. Some other cases require further thought and consist of modeling a physical situation, simplifying the original problem and reaching a solution. Guidelines are given in order to help the reader to solve the presented problem. It is worth noting that, in most cases, there is no unique solution to a given problem. In fact, a solution results from a series of simple assumptions, which enable rather simple calculations. The object of the book is to facilitate studying flows with heat transfer and to propose some methods to calculate them. It is obvious that numerical modeling and the use of commercial software now enable the treatment of problems much more complex than those presented here. Nevertheless, it seems to us that solving simple problems is vital in order to acquire a solid background in the domain. This is a necessary step in order to consistently design systems or to correctly interpret results of the physical or numerical experiments from a critical point of view.

Industrial projects and geophysical situations involve relatively complex phenomena and raise problems with a degree of difficulty depending on the specificity of the case under consideration. We restrict the study of the convective heat transfer phenomena in this book to the following set of assumptions:

– single-phase flows with one constituent;

– Newtonian fluid;

– incompressible flows;

– negligible radiation;

– constant fluid physical properties;

– negligible dissipation.

However, in Chapter 1 only the last two points will be discussed.

The first chapter presents the fundamental equations that apply with the above list of assumptions, to convective heat transfer and reviews the main dimensionless numbers in this topic.

Most flows present in industrial applications or in the environment are turbulent so that a large section at the end of the book is devoted to turbulent transfer. The study of laminar flows with heat transfer is, however, a necessary first step to understanding the physical mechanisms governing turbulent transfer. Moreover, several applications are concerned with laminar flows. This is the reason why we present convective heat transfer in fully developed laminar flows in Chapter 2.

A good knowledge of boundary layers is extremely important to understanding convective heat transfer, which most usually concerns flows in the vicinity of heated or cooled walls. Consequently, Chapter 3 is devoted to these flows and several problems are devoted to related issues. This chapter is complemented by the next one, which is concerned with heat transfer in flows around obstacles.

Chapters 5 and 6 deal with natural convection in external and internal flows. The coupling between the flow field and heat transfer makes the corresponding problems difficult and we present some important examples to clarify the key points relative to this problem.

Turbulent transfer is presented in Chapters 7 to 9, for flows in channels and ducts, in boundary layers and finally in free shear flows.

Scale analysis [BEJ 95] is widely used in this textbook. It is quite an efficient tool to use to get insight into the role played by the group of parameters of a given physical situation. Scale analysis leads to the relevant dimensionless numbers and enables a quick determination of the expected trends. The information given by this analysis may be used as a guideline for simplifying the equations when a theoretical model is implemented and for interpreting the results of numerical simulations or physical experiments. This approach has the notable advantage of enabling substantial economy in the number of studied cases since it is sufficient to vary few dimensionless numbers instead of all the parameters to specify their influence on, for example, a heat transfer law.

Other classical methods of solving are presented in the review of the theoretical principles and are used in the presented problems (autosimilarity solutions, integral method).

This book is addressed to MSc students in universities or engineering schools. We hope that it will also be useful to engineers and developers confronted with convective heat transfer problems.

Chapter 1

Fundamental Equations, Dimensionless Numbers

1.1. Fundamental equations

The equations applying to incompressible flows and associated heat transfer are recalled hereafter. The meaning of symbols used in the fundamental equations is given in the following sections, otherwise the symbols are listed at the end of the book.

1.1.1. Local equations

The local equations express the conservation principles for a fluid particle in motion. The operator d/dt represents the Lagrangian derivative or material derivative of any physical quantity. It corresponds to the derivative of this quantity as measured by an observer following the fluid particle:

[1.1]

1.1.1.1. Mass conservation

The continuity equation expresses the mass conservation for a moving fluid particle as:

[1.2]

For the applications presented in this book, the density ρ may be considered as constant so that the continuity equation reduces to:

[1.3]

1.1.1.2. Navier-Stokes equations

The Navier-Stokes equations express the budget of momentum for a fluid particle. Without loss of generality, we can write:

[1.4]

where represents the body force vector per unit mass (the most usual example is that of gravity, with is the stress tensor, expressed with index notations for a Newtonian fluid by:

[1.5]

In equation [1.5], δij is the Kronecker symbol and dij is the pure strain tensor

The Navier-Stokes equations are then obtained for an incompressible flow of a fluid with constant dynamic viscosity μ. They are expressed in vector notations as:

[1.6]

1.1.1.3. Energy equation

Inside a flow, a fluid particle exchanges heat by conduction with the neighbouring particles during its motion. It also exchanges heat by radiation with the environment, but this mode of transfer is not covered in this book.

The conductive heat transfer is governed by Fourier’s1 law:

[1.7]

where is the heat flux vector at a current position. Its components are expressed in W/m2. The heat transfer rate flowing through a surface element dS of normal is Combining the first principle of thermodynamics, the kinetic energy equation, Fourier’s law, and introducing some fluid physical properties, the energy equation is obtained without loss of generality as: