(bq) part 1 book fundementals of heat and mass transfer kotandaraman has contents: an overview of heat transfer, steady state conduction, conduction with heat generation, heat transfer with extended surfaces (fins), two dimensional steady heat conduction, two dimensional steady heat conduction.
This page intentionally left blank Copyright © 2006, 1999, 1994, New Age International (P) Ltd., Publishers Published by New Age International (P) Ltd., Publishers All rights reserved No part of this ebook may be reproduced in any form, by photostat, microfilm, xerography, or any other means, or incorporated into any information retrieval system, electronic or mechanical, without the written permission of the publisher All inquiries should be emailed to rights@newagepublishers.com ISBN (13) : 978-81-224-2642-7 PUBLISHING FOR ONE WORLD NEW AGE INTERNATIONAL (P) LIMITED, PUBLISHERS 4835/24, Ansari Road, Daryaganj, New Delhi - 110002 Visit us at www.newagepublishers.com PREFACE TO THE THIRD EDITION Professor Obert has observed in his famous treatise on Thermodynamics that concepts are better understood by their repeated applications to real life situations A firm conviction of this principle has prompted the author to arrange the text material in each chapter in the following order In the first section after enunciating the basic concepts and laws mathematical models are developed leading to rate equations for heat transfer and determination of temperature field, simple and direct numerical examples are included to illustrate the basic laws More stress is on the model development as compared to numerical problems A section titled “SOLVED PROBLEMS” comes next In this section more involved derivations and numerical problems of practical interest are solved The investigation of the effect of influencing parameters for the complete spectrum of values is attempted here Problems involving complex situations are shown solved in this section Two important ideas are stressed in this section These are checking of dimensional homogeneity in the case of all equations derived and the validation of numerical answers by cross checking This concept of validation in professional practice is a must in all design situations In the next section objective type questions are given These are very useful for understanding the basis and resolving misunderstandings In the final section a large number of graded exercise problems involving simple to complex situations are included In the first of the 14 chapters the basic laws for the three modes of heat transfer are introduced and the corresponding rate equations are developed The use of electrical analogy is introduced and applied to single and multimode heat transfer situations The need for iterative working is stressed in the solved problems The second chapter deals with one dimensional steady state conduction Mathematical models are developed by the three geometries namely Plate, Hollow Cylinder and Hollow Sphere Multilayer insulation is also discussed The effect of variation of thermal conductivity on heat transfer and temperature field is clearly brought out Parallel flow systems are discussed Examples on variation of area along the heat flow direction are included The use of electrical analogy is included in all the worked examples The importance of calculating the temperature gradient is stressed in many of the problems In the third chapter models for conduction with heat generation are developed for three geometric configurations namely plate, cylinder and sphere The effect of volume to surface area and the convection coefficient at the surface in maintaining lower material temperature is illustrated Hollow cylindrical shape with different boundary conditions is discussed Conduction with variable heat generation rate is also modelled Fins/extended surface or conduction-convection situation is discussed in the fourth chapter Models for heat transfer and temperature variation are developed for four different vi PREFACE boundary conditions Optimisation of the shape of the fin of specified volume for maximum heat flow is discussed Circumferential fins and variable area fins are analysed The use of numerical method is illustrated Error in measurement of temperature using thermometer is well discussed The possibility of measurement of thermal conductivity and convective heat transfer coefficient using fins is illustrated Two dimensional steady state conduction is discussed in the fifth chapter Exact analysis is first developed for two types of boundary conditions The use of numerical method is illustrated by developing nodal equations The concept and use of conduction shape factor is illustrated for some practical situations One dimensional transient (unsteady) heat conduction is discussed in Chapter Three types of models arise in this case namely lumped heat capacity system, semi-infinite solid and infinite solid Lumped heat capacity model for which there are a number of industrial applications is analysed in great detail and problems of practical interest are shown solved The condition under which semi-infinite solid model is applicable as compared to infinite solid model is clearly explained Three types of boundary conditions are analysed Infinite solid model for three geometric shapes is analysed next The complexity of the analytical solution is indicated Solution using charts is illustrated in great detail Real solids are of limited dimensions and these models cannot be applied directly in these cases In these cases product solution is applicable A number of problems of practical interest for these types of solids are worked out in this section In both cases a number of problems are solved using numerical methods Periodic heat flow problems are also discussed Concepts and mechanism of convection are discussed in the seventh chapter After discussing the boundary layer theory continuity, momentum and energy equations are derived Next the different methods of solving these equations are discussed In addition to the exact analysis approximate integral method, analogy method and dimensional analysis are also discussed and their applicability is indicated General correlations for convective heat transfer coefficient in terms of dimensionless numbers are arrived at in this chapter In Chapter 8, in addition to the correlations derived in the previous chapter, empirical correlations arrived at from experimental results are listed and applied to flow over surfaces like flat plate, cylinder, sphere and banks of tubes Both laminar and turbulent flows situation are discussed Flow through ducts is discussed in Chapter Empirical correlations for various situations are listed Flow developing region, fully developed flow conditions, constant wall temperature and constant wall heat flux are some of the conditions analysed Flow through non-circular pipes and annular flow are also discussed in this chapter Natural convection is dealt with in Chapter 10 Various geometries including enclosed space are discussed The choice of the appropriate correlation is illustrated through a number of problems Combined natural and forced convection is also discussed Chapter 11 deals with phase change processes Boiling, condensation, freezing and melting are discussed Basic equations are derived in the case of freezing and melting and condensation The applicable correlations in boiling are listed and their applicability is illustrated through numerical examples Chapter 12 deals with heat exchangers, both recuperative and regenerative types The LMTD and NTU-effectiveness methods are discussed in detail and the applicability of these methods is illustrated Various types of heat exchangers are compared for optimising the size PREFACE vii Thermal radiation is dealt with in Chapter 13 The convenience of the use of electrical analogy for heat exchange among radiating surfaces is discussed in detail and is applied in almost all the solved problems Gas radiation and multi-body enclosures are also discussed Chapter 14 deals with basic ideas of mass transfer in both diffusion and convection modes A large number of problems with different fluid combinations are worked out in this chapter A large number of short problems and fill in the blank type and true or false type questions are provided to test the understanding of the basic principles Author This page intentionally left blank CONTENTS v Preface to the Third Edition AN OVERVIEW OF HEAT TRANSFER 1–25 1.0 Introduction 1.1 Heat Transfer 1.2 Modes of Heat Transfer 1.3 Combined Modes of Heat Transfer 1.4 Dimensions and Units 10 1.5 Closure 11 Solved Problems 11 Exercise Problems 22 STEADY STATE CONDUCTION 26–98 2.0 2.1 2.2 2.3 2.4 Conduction 26 The General Model for Conduction Study 26 Steady Conduction in One Direction (One Dimensional) 30 Conduction in Other Shapes 41 One Dimensional Steady State Heat Conduction with Variable Heat Conductivity or Variable Area Along the Section 42 2.5 Critical Thickness of Insulation 48 2.6 Mean Area Concept 50 2.7 Parallel Flow 51 Solved Problems 53 Objective Questions 92 Exercise Problems 93 CONDUCTION WITH HEAT GENERATION 3.0 3.1 99–127 Introduction 99 Steady State One Dimensional Conduction in a Slab with Uniform Heat Generation 99 3.2 Steady State Radial Heat Conduction in Cylinder with Uniform Heat Generation 103 3.3 Radial Conduction in Sphere with Uniform Heat Generation 107 3.4 Conclusion 109 Solved Problems 110 Objective Questions 125 Exercise Problems 125 ... 1. 10 1. 11 1 .12 1. 13 1. 14 1. 15 1. 16 1. 17 1. 18 1. 19 1. 20 1. 21 1.22 1. 23 1. 24 1. 25 FUNDAMENTALS OF HEAT AND MASS TRANSFER A sphere of 0.5m diameter containing hot fluid has an insulation of 0.1m thickness... OVERVIEW OF HEAT TRANSFER 1? ??25 1. 0 Introduction 1. 1 Heat Transfer 1. 2 Modes of Heat Transfer 1. 3 Combined Modes of Heat Transfer 1. 4 Dimensions and Units 10 1. 5 Closure 11 Solved Problems 11 Exercise... T1 – c1x1 = T1 – T1 − T2 x1 x1 − x Substituting in the general solution T= ∴ T – T1 = T1 − T2 T − T2 x + T1 – x x1 − x x1 − x T1 − T2 (x – x1) x1 − x or T − T1 x − x1 = T1 − T2 x1 − x or T1