A Textbook of Metallurgical Kinetics

A Textbook of Metallurgical Kinetics

A Textbook of Metallurgical Kinetics AHINDRA GHOSH Formerly Professor Materials and Metallurgical Engineering Indian Institute of Technology Kanpur SUDIPTO GHOSH Associate Professor Metallurgical and Materials Engineering Indian Institute of Technology Kharagpur Delhi-110092 2014

A Textbook of Metallurgical Kinetics Ahindra Ghosh and Sudipto Ghosh 2014 by PHI Learning Private Limited, Delhi. All rights reserved. No part of this book may be reproduced in any form, by mimeograph or any other means, without permission in writing from the publisher. ISBN-978-81-203-4828-8 The export rights of this book are vested solely with the publisher. Published by Asoke K. Ghosh, PHI Learning Private Limited, Rimjhim House, 111, Patparganj Industrial Estate, Delhi-110092 and Printed by Mudrak, 30-A, Patparganj, Delhi-110091.

To (Late) Professor Carl Wagner A Pioneer of Metallurgical Kinetics and A Source of Inspiration

Contents Preface xiii List of Symbols with Units xv 1. Introduction 1 10 1.1 Thermodynamics and Kinetics 1 1.2 Homogeneous and Heterogeneous Reactions and Processes 3 1.3 Kinetics of Metallurgical Reactions and Processes at High Temperatures 3 1.4 Kinetics of Heterogeneous Reactions Introductory Concepts 4 1.4.1 Kinetic Steps 4 1.4.2 Three-phase and Multi-phase Reactions 5 1.5 Rate-controlling Step 5 1.6 Concept of Virtual Maximum Rate 6 1.7 Values of Some Physical Constants 9 Problems 10 Reference 10 2. Kinetics of Homogeneous Chemical Reactions 11 29 2.1 Variation of Reaction Rate with Concentration 11 2.1.1 General Features 11 2.1.2 Law of Mass Action 12 2.1.3 Reactions Occurring in Stages 14 2.1.4 Integrated Rate Equations 15 2.2 Variation of Rate Constant with Temperature Rate Theory 17 2.2.1 General 17 2.2.2 The Arrhenius Equation 18 2.2.3 Significance and Theoretical Estimation of Activation Energy 21 2.2.4 The Collision Theory 23 2.3 Theory of Absolute Reaction Rates 23 2.3.1 Statistical Mechanics of Chemical Equilibrium 24 vii

viii Contents 2.3.2 Derivation of the Theory of Absolute Reaction Rates 25 2.4 Application of the Theory of Absolute Reaction Rates 26 2.4.1 Thermodynamic Formulation of Reaction Rates 27 2.4.2 Arrhenius Equation and the Absolute Reaction Rate Theory 28 Problems 28 References 29 3. Gas Solid and Gas Liquid Interfacial Reactions 30 53 3.1 Adsorption 32 3.1.1 Physical Adsorption 32 3.1.2 Chemisorption 32 3.2 Adsorption Isotherms 33 3.2.1 Langmuir Adsorption Isotherm 33 3.2.2 Gibbs Adsorption Isotherm 35 3.3 Examples of Slow Surface Reaction in High Temperature Metallurgy 38 3.3.1 Gasification of Carbon by Carbon Dioxide 39 3.3.2 Kinetics of Nitrogen Transfer across Iron Surface 42 3.4 Some Miscellaneous Topics 48 3.4.1 Role of Thermodynamic Activity of Adsorbed Atomic Species 48 3.4.2 Maximum Possible Rate of Surface Reaction with Gas 50 Problems 52 References 53 4. Diffusion 54 81 4.1 Fick s First Law of Diffusion 54 4.1.1 A Note on Diffusion Coefficient 55 4.2 Generalized Diffusion Equation 55 4.3 Steady-state Diffusion One-dimensional Cases 58 4.3.1 Diffusion through an Infinite Flat Plate 59 4.3.2 Steady Diffusion through an Infinitely Long Hollow Cylinder 61 4.3.3 Steady Diffusion through a Hollow Sphere 62 4.4 Pseudo-steady Diffusion 64 4.5 Unsteady-state Diffusion One-dimensional Cases 65 4.5.1 Unsteady Diffusion in an Infinite Flat Plate 65 4.5.2 Radial Diffusion in Infinitely Long Cylinder 69 4.5.3 Radial Diffusion in Solid Sphere 70 4.5.4 Semi-infinite Rectangular Specimen 70 4.5.5 Applications of Unsteady Diffusion Equations 74 4.6 Diffusion Coefficient Some Introductory Remarks 76 4.6.1 Diffusion in Ideal Gases 77 4.6.2 Diffusion in Solids and Liquids 77 4.6.3 Diffusion of Gases through Pores in Solids 78 Problems 79 References 81

Contents ix 5. Applications of Diffusion Equations 82 100 5.1 Examples of Pseudo-steady Diffusion 82 5.1.1 High Temperature Oxidation of Metals and Alloys 82 5.1.2 Reaction of a Sphere of Porous Solid with Gas 86 5.2 Examples of Unsteady Diffusion 89 5.2.1 Carburizing and Decarburizing of Steel Consisting of Two Phases 89 5.2.2 Simultaneous Isothermal Scaling and Decarburization 94 5.2.3 Internal Oxidation of Alloys 97 References 100 6. Convection, Mass Transfer and Mixing in Fluids 101 123 6.1 Nature of Fluid Motion 101 6.2 Mass Transfer under Laminar Flow 103 6.2.1 Equimolal Counter-diffusion 104 6.2.2 Transfer of One Species through Another Stagnant Species 106 6.3 Mass Transfer in Turbulent Flow 111 6.4 Turbulence and Mixing 112 6.4.1 Basics of Turbulence 113 6.4.2 Eddy Diffusion Dispersion Models of Mixing 114 6.4.3 Metal Mixing in Open-hearth Steelmaking 115 6.4.4 Fluid Flow and Mixing in Gas-stirred Ladle 118 Problems 122 References 122 7. Mass Transfer in Fluid at Solid Fluid Interface 124 150 7.1 Boundary Layer and Mass Transfer Coefficient 124 7.1.1 Velocity Boundary Layer 125 7.1.2 Concentration Boundary Layer and Mass Transfer Coefficient 126 7.1.3 Some Notes on Use of Mass Transfer Coefficient 127 7.2 Variables Influencing k m and Dimensionless Groups in Convective Mass Transfer 129 7.3 Momentum Heat Mass Transfer Analogy 134 7.3.1 Momentum Flux 134 7.3.2 Heat Flux; Heat Transfer Coefficient 135 7.3.3 Mass Flux; Mass Transfer Coefficient 136 7.3.4 The Analogy 136 7.4 Analytical Solution of Mass Transfer Correlations 137 7.5 Application in Studies of Pyro-Metallurgical Reactions 141 7.5.1 Reduction of SiO 2 in Reducing Gases 141 7.5.2 Dissolution of Carbon Steel in Molten Iron Carbon Alloys 143 7.5.3 Dissolution of Nickel Cylinder in Molten Aluminium under Free Convection 144 7.5.4 Some Remarks on Dissolution Kinetics 146 7.6 Penetration of Turbulence in Boundary Layer 147 Problems 149 References 149

A Textbook Of Metallurgical Kinetics 30% OFF Publisher : PHI Learning ISBN : 9788120348288 Author : Ahindra Ghosh, Sudipto Ghosh Type the URL : http://www.kopykitab.com/product/7606 Get this ebook