A Textbook of Metallurgical Kinetics

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2 A Textbook of Metallurgical Kinetics

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4 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

5 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 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 and Printed by Mudrak, 30-A, Patparganj, Delhi

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

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8 Contents Preface xiii List of Symbols with Units xv 1. Introduction Thermodynamics and Kinetics Homogeneous and Heterogeneous Reactions and Processes Kinetics of Metallurgical Reactions and Processes at High Temperatures Kinetics of Heterogeneous Reactions Introductory Concepts Kinetic Steps Three-phase and Multi-phase Reactions Rate-controlling Step Concept of Virtual Maximum Rate Values of Some Physical Constants 9 Problems 10 Reference Kinetics of Homogeneous Chemical Reactions Variation of Reaction Rate with Concentration General Features Law of Mass Action Reactions Occurring in Stages Integrated Rate Equations Variation of Rate Constant with Temperature Rate Theory General The Arrhenius Equation Significance and Theoretical Estimation of Activation Energy The Collision Theory Theory of Absolute Reaction Rates Statistical Mechanics of Chemical Equilibrium 24 vii

9 viii Contents Derivation of the Theory of Absolute Reaction Rates Application of the Theory of Absolute Reaction Rates Thermodynamic Formulation of Reaction Rates Arrhenius Equation and the Absolute Reaction Rate Theory 28 Problems 28 References Gas Solid and Gas Liquid Interfacial Reactions Adsorption Physical Adsorption Chemisorption Adsorption Isotherms Langmuir Adsorption Isotherm Gibbs Adsorption Isotherm Examples of Slow Surface Reaction in High Temperature Metallurgy Gasification of Carbon by Carbon Dioxide Kinetics of Nitrogen Transfer across Iron Surface Some Miscellaneous Topics Role of Thermodynamic Activity of Adsorbed Atomic Species Maximum Possible Rate of Surface Reaction with Gas 50 Problems 52 References Diffusion Fick s First Law of Diffusion A Note on Diffusion Coefficient Generalized Diffusion Equation Steady-state Diffusion One-dimensional Cases Diffusion through an Infinite Flat Plate Steady Diffusion through an Infinitely Long Hollow Cylinder Steady Diffusion through a Hollow Sphere Pseudo-steady Diffusion Unsteady-state Diffusion One-dimensional Cases Unsteady Diffusion in an Infinite Flat Plate Radial Diffusion in Infinitely Long Cylinder Radial Diffusion in Solid Sphere Semi-infinite Rectangular Specimen Applications of Unsteady Diffusion Equations Diffusion Coefficient Some Introductory Remarks Diffusion in Ideal Gases Diffusion in Solids and Liquids Diffusion of Gases through Pores in Solids 78 Problems 79 References 81

10 Contents ix 5. Applications of Diffusion Equations Examples of Pseudo-steady Diffusion High Temperature Oxidation of Metals and Alloys Reaction of a Sphere of Porous Solid with Gas Examples of Unsteady Diffusion Carburizing and Decarburizing of Steel Consisting of Two Phases Simultaneous Isothermal Scaling and Decarburization Internal Oxidation of Alloys 97 References Convection, Mass Transfer and Mixing in Fluids Nature of Fluid Motion Mass Transfer under Laminar Flow Equimolal Counter-diffusion Transfer of One Species through Another Stagnant Species Mass Transfer in Turbulent Flow Turbulence and Mixing Basics of Turbulence Eddy Diffusion Dispersion Models of Mixing Metal Mixing in Open-hearth Steelmaking Fluid Flow and Mixing in Gas-stirred Ladle 118 Problems 122 References Mass Transfer in Fluid at Solid Fluid Interface Boundary Layer and Mass Transfer Coefficient Velocity Boundary Layer Concentration Boundary Layer and Mass Transfer Coefficient Some Notes on Use of Mass Transfer Coefficient Variables Influencing k m and Dimensionless Groups in Convective Mass Transfer Momentum Heat Mass Transfer Analogy Momentum Flux Heat Flux; Heat Transfer Coefficient Mass Flux; Mass Transfer Coefficient The Analogy Analytical Solution of Mass Transfer Correlations Application in Studies of Pyro-Metallurgical Reactions Reduction of SiO 2 in Reducing Gases Dissolution of Carbon Steel in Molten Iron Carbon Alloys Dissolution of Nickel Cylinder in Molten Aluminium under Free Convection Some Remarks on Dissolution Kinetics Penetration of Turbulence in Boundary Layer 147 Problems 149 References 149

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