Hans Dieter Baehr · Karl Stephan Heat and Mass Transfer Hans Dieter Baehr · Karl Stephan Heat and Mass Transfer Second, revised Edition With 327 Figures 123 Dr. Hans Dieter Baehr Professor em. of Thermodynamics, University of Hannover, Germany Dr. Karl Stephan Professor (em.) Institute of Thermodynamics and Thermal Process Engineering University of Stuttgart 70550 Stuttgart Germany e-mail: stephan@itt.de Library of Congress Control Number: 2006922796 ISBN-10 3-540-29526-7 Second Edition Springer Berlin Heidelberg New York ISBN-13 978-3-540-29526-6 Second Edition Springer Berlin Heidelberg New York ISBN 3-540-63695-1 First Edition Springer-Verlag 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. 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 1998, 2006 Printed in Germany 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. Typesetting: Digital data supplied by authors Cover Design: medionet, Berlin Production: LE-TEX Jelonek, Schmidt & Vöckler GbR, Leipzig Printed on acid-free paper 7/3100/YL 543210 Preface to the second edition In this revised edition of our book we retained its concept: The main empha- sis is placed on the fundamental principles of heat and mass transfer and their application to practical problems of process modelling and the apparatus design. Like the first edition, the second edition contains five chapters and several appendices, particularly a compilation of thermophysical property data needed for the solution of problems. Changes are made in those chapters presenting heat and mass transfer correlations based on theoretical results or experimental findings.
They were adapted to the most recent state of our knowledge. Some of the worked examples, which should help to deepen the comprehension of the text, were revised or updated as well. The compilation of the thermophysical property data was revised and adapted to the present knowledge. Solving problems is essential for a sound understanding and for relating prin- ciples to real engineering situations.
Numerical answers and hints to the solution of problems are given in the final appendix. The new edition also enabled us to correct printing errors and mistakes. In preparing the new edition we were assisted by Jens Körber, who helped us to submit a printable version of the manuscript to the publisher. We owe him sincere thanks.
We also appreciate the efforts of friends and colleagues who provided their good advice with constructive suggestions. Bochum and Stuttgart, H. Stephan Preface to the first edition This book is the English translation of our German publication, which appeared in 1994 with the title “Wärme und Stoffübertragung” (2nd edition Berlin: Springer Verlag 1996). The German version originated from lecture courses in heat and mass transfer which we have held for many years at the Universities of Hannover and Stuttgart, respectively.
Our book is intended for students of mechanical and chemical engineering at universities and engineering schools, but will also be of use to students of other subjects such as electrical engineering, physics and chemistry. Firstly our book should be used as a textbook alongside the lecture course. Its intention is to make the student familiar with the fundamentals of heat and mass transfer, and enable him to solve practical problems. On the other hand we placed special emphasis on a systematic development of the theory of heat and mass transfer and gave extensive discussions of the essential solution methods for heat and mass transfer problems.
Therefore the book will also serve in the advanced training of practising engineers and scientists and as a reference work for the solution of their tasks. The material is explained with the assistance of a large number of calculated examples, and at the end of each chapter a series of exercises is given. This should also make self study easier. Many heat and mass transfer problems can be solved using the balance equa- tions and the heat and mass transfer coefficients, without requiring too deep a knowledge of the theory of heat and mass transfer.
Such problems are dealt with in the first chapter, which contains the basic concepts and fundamental laws of heat and mass transfer. The student obtains an overview of the different modes of heat and mass transfer, and learns at an early stage how to solve practical problems and to design heat and mass transfer apparatus. This increases the mo- tivation to study the theory more closely, which is the object of the subsequent chapters. In the second chapter we consider steady-state and transient heat conduction and mass diffusion in quiescent media.
The fundamental differential equations for the calculation of temperature fields are derived here. We show how analytical and numerical methods are used in the solution of practical cases. Alongside the Laplace transformation and the classical method of separating the variables, we have also presented an extensive discussion of finite difference methods which are very important in practice. Many of the results found for heat conduction can be transferred to the analogous process of mass diffusion.
The mathematical solution formulations are the same for both fields. viii Preface The third chapter covers convective heat and mass transfer. The derivation of the mass, momentum and energy balance equations for pure fluids and multi- component mixtures are treated first, before the material laws are introduced and the partial differential equations for the velocity, temperature and concentration fields are derived. As typical applications we consider heat and mass transfer in flow over bodies and through channels, in packed and fluidised beds as well as free convection and the superposition of free and forced convection.
Finally an introduction to heat transfer in compressible fluids is presented. In the fourth chapter the heat and mass transfer in condensation and boil- ing with free and forced flows is dealt with. The presentation follows the book, “Heat Transfer in Condensation and Boiling” (Berlin: Springer-Verlag 1992) by K. Here, we consider not only pure substances; condensation and boiling in mixtures of substances are also explained to an adequate extent.
Thermal radiation is the subject of the fifth chapter. It differs from many other presentations in so far as the physical quantities needed for the quantita- tive description of the directional and wavelength dependency of radiation are extensively presented first. Only after a strict formulation of Kirchhoff’s law, the ideal radiator, the black body, is introduced. After this follows a discussion of the material laws of real radiators.
Solar radiation and heat transfer by radiation are considered as the main applications. An introduction to gas radiation, important technically for combustion chambers and furnaces, is the final part of this chapter. As heat and mass transfer is a subject taught at a level where students have already had courses in calculus, we have presumed a knowledge of this field. Those readers who only wish to understand the basic concepts and become familiar with simple technical applications of heat and mass transfer need only study the first chapter.
More extensive knowledge of the subject is expected of graduate mechanical and chemical engineers. The mechanical engineer should be familiar with the fundamentals of heat conduction, convective heat transfer and radiative transfer, as well as having a basic knowledge of mass transfer. Chemical engineers also require, in addition to a sound knowledge of these areas, a good understanding of heat and mass transfer in multiphase flows. The time set aside for lectures is generally insufficient for the treatment of all the material in this book.
However, it is important that the student acquires a broad understanding of the fundamentals and methods. Then it is sufficient to deepen this knowledge with selected examples and thereby improve problem solving skills. In the preparation of the manuscript we were assisted by a number of our colleagues, above all by Nicola Jane Park, MEng., University of London, Imperial College of Science, Technology and Medicine. We owe her sincere thanks for the translation of our German publication into English, and for the excellent cooperation.
Hannover and Stuttgart, H. Stephan Contents Nomenclature xvi 1 Introduction.1 The different types of heat transfer .2 Steady, one-dimensional conduction of heat .3 Convective heat transfer. Heat transfer coefficient .4 Determining heat transfer coefficients.2 Overall heat transfer .1 The overall heat transfer coefficient .2 Multi-layer walls .3 Overall heat transfer through walls with extended surfaces .4 Heating and cooling of thin walled vessels .1 Types of heat exchanger and flow configurations .2 General design equations.3 Countercurrent and cocurrent heat exchangers .4 Crossflow heat exchangers .5 Operating characteristics of further flow configurations.4 The different types of mass transfer .1 Composition of mixtures .2 Diffusive fluxes .2 Diffusion through a semipermeable plane. Equimolar diffusion .3 Convective mass transfer .5 Mass transfer theories .2 Boundary layer theory .3 Penetration and surface renewal theories .4 Application of film theory to evaporative cooling .6 Overall mass transfer .7 Mass transfer apparatus .2 Concentration profiles and heights of mass transfer columns.
101 2 Heat conduction and mass diffusion 105 2.1 The heat conduction equation .1 Derivation of the differential equation for the temperature field .2 The heat conduction equation for bodies with constant material properties .4 Temperature dependent material properties .5 Similar temperature fields .2 Steady-state heat conduction .1 Geometric one-dimensional heat conduction with heat sources .2 Longitudinal heat conduction in a rod .3 The temperature distribution in fins and pins .5 Geometric multi-dimensional heat flow .1 Superposition of heat sources and heat sinks .3 Transient heat conduction .2 The Laplace transformation .3 The semi-infinite solid .1 Heating and cooling with different boundary conditions .2 Two semi-infinite bodies in contact with each other .3 Periodic temperature variations .4 Cooling or heating of simple bodies in one-dimensional heat flow .1 Formulation of the problem .2 Separating the variables .3 Results for the plate .4 Results for the cylinder and the sphere .5 Approximation for large times: Restriction to the first term in the series .6 A solution for small times .5 Cooling and heating in multi-dimensional heat flow .2 Approximation for small Biot numbers .6 Solidification of geometrically simple bodies .1 The solidification of flat layers (Stefan problem) .2 The quasi-steady approximation .1 Homogeneous heat sources .2 Point and linear heat sources .4 Numerical solutions to heat conduction problems .1 The simple, explicit difference method for transient heat conduction problems .1 The finite difference equation .2 The stability condition .2 Discretisation of the boundary conditions .3 The implicit difference method from J. Temperature dependent material properties .1 The discretisation of the self-adjoint differential operator .2 Constant material properties.3 Temperature dependent material properties .5 Transient two- and three-dimensional temperature fields .6 Steady-state temperature fields .1 A simple finite difference method for plane, steady-state temperature fields .2 Consideration of the boundary conditions .5 Mass diffusion .1 Remarks on quiescent systems .2 Derivation of the differential equation for the concentration field .5 Steady-state mass diffusion with catalytic surface reaction .6 Steady-state mass diffusion with homogeneous chemical reaction .7 Transient mass diffusion .1 Transient mass diffusion in a semi-infinite solid .2 Transient mass diffusion in bodies of simple geometry with one-dimensional mass flow. 246 3 Convective heat and mass transfer. Single phase flow 253 3.1 Preliminary remarks: Longitudinal, frictionless flow over a flat plate .2 The balance equations .1 Reynolds’ transport theorem .2 The mass balance .3 The momentum balance .1 The stress tensor .2 Cauchy’s equation of motion .3 The strain tensor .4 Constitutive equations for the solution of the momentum equation .5 The Navier-Stokes equations .4 The energy balance .1 Dissipated energy and entropy .