Fundamental of Transport Phenomena and Metallurgical Process Modeling

Preface
Contents
About the Author
Symbols
1 Fluid Dynamics
1.1 Basic Concept
1.2 Fluid Dynamics
1.2.1 Newton’s Law of Viscosity
1.2.2 Flow Characterization
1.2.3 Velocity Profile
1.2.4 Velocity Boundary Layer
1.2.5 Pressure at a Point in Static Fluid
1.2.6 Pressure Variation in Static Fluid
1.2.7 Buoyancy Forces
1.3 Energy Balance
1.3.1 Chemical Analysis Laboratory
1.3.2 Water Tank with Pump for Water Supply
1.3.3 Water Tank with Pump for Water Supply to the Tank at Roof
1.3.4 General Equation for Overall Energy Balance
1.3.5 Applications of Overall Energy Balance
1.3.6 Other Application
1.3.7 Overall Mass Balance
1.4 Exercises
1.5 Questions
References
2 Mass and Momentum Balances
2.1 Introduction
2.2 Different Types of Derivatives
2.2.1 Simple Derivative ( dfdt )
2.2.2 Partial Time Derivative ( δt )
2.2.3 Total Time Derivative ( ddt )
2.2.4 Substantial Time Derivative ( DDt )
2.3 Differential Mass Balance (Continuity Equation)
2.3.1 Continuity Equation for Steady State
2.3.2 Continuity Equation for Incompressible Fluid
2.4 Differential Momentum Balance or Equation of Motion
2.5 Application of Continuity and Navier–Stokes Equations
2.5.1 Flow of Falling Fluid
2.5.2 Axial Flow Through Pipe
2.5.3 High Speed Flow of Gases
2.6 Mechanism of Momentum Transport
2.7 Dimensional Analysis
2.7.1 Methods of Dimensional Analysis
2.8 Friction Factor
2.9 Laminar, Steady Flow Around Submerged Solid Sphere
2.9.1 Fluid Flow in Circular Pipe
2.10 Fluid Flow Through Packed Bed of Solids
2.11 Overall Force Balance for Packed Bed of Solids
2.12 Exercises
2.13 Questions
References
3 Heat Transfer
3.1 Basic Concept
3.2 Temperature Field
3.3 Conduction
3.3.1 Fourier’s Law
3.3.2 Thermal Conductivity
3.4 Convection
3.5 Radiation
3.6 Concept of Driving Potential
3.7 Combined Mechanism of Heat Transfer
3.7.1 Heat Transfer by Combined Convection and Conduction Modes
3.7.2 Heat Transfer by Combination of Three Modes
3.8 General Differential Equation of Heat Conduction
3.8.1 Cartesian Coordinates System
3.8.2 Cylindrical Coordinates System
3.8.3 Spherical Coordinates System
3.9 One-Dimensional Heat Conduction
3.9.1 Plane Wall
3.9.2 Heat Conduction Through Cylindrical System
3.9.3 Heat Conduction Through Spherical System
3.10 Systems with Variable Thermal Conductivity
3.10.1 Plane Wall (Slab)
3.10.2 Hollow Cylinder
3.10.3 Hollow Sphere
3.11 Composite Systems
3.11.1 Series Composite Plane Walls
3.11.2 Series–Parallel Composite Walls
3.11.3 Coaxial Cylinder
3.11.4 Coaxial Sphere
3.11.5 Critical Radius of Insulation
3.12 Systems with Different Heat Sources
3.12.1 Plane Wall with Internal Heat Generation
3.12.2 Hollow Cylinder with Internal Heat Generation
3.12.3 Solid Cylinder with Internal Heat Generation
3.12.4 Solid Sphere with Internal Heat Generation
3.13 Convective Heat Transfer
3.13.1 Natural Convective Heat Transfer
3.13.2 Forced Convective Heat Transfer
3.14 Thermal Radiation
3.14.1 Absorption, Reflection, and Transmission
3.14.2 Concept of Black Body
3.14.3 Radiation from Non-black Surfaces
3.15 Exercises
3.16 Questions
References
4 Mass Transfer
4.1 Basic Concept
4.2 Mass Transfer
4.2.1 Mass Transfer by Diffusion
4.3 General Mass Diffusion Equation
4.3.1 Steady-State Diffusion Through Plain Membrane
4.3.2 Steady-State Equimolar Counter Diffusion
4.3.3 Mass Diffusion Through Stagnant Fluid
4.4 Diffusion of Gas Through Solid
4.5 Motion of Gas Bubbles in Liquid
4.6 Mechanism of Mass Transfer
4.7 Simultaneous Heat and Mass Transfer
4.7.1 Change of Phase Due to Melting
4.7.2 Heat and Mass Transfer to Single Particle
4.8 Exercises
4.9 Questions
References
5 Basic Concept of Models
5.1 Basic Concept
5.2 Physical Model
5.2.1 Development of Rigorous Physical Model
5.2.2 Techniques for Ensuring Similarity
5.2.3 Development of Semi-Rigorous Physical Model
5.2.4 Preliminary Ad Hoc Measurements
5.3 Mathematical Modeling
5.3.1 Classification of Mathematical Models
5.4 Development of Mathematical Model
5.4.1 Components of Mathematical Model
5.4.2 Role of Mathematical Model in Process Analysis
5.4.3 Developing of Mathematical Model
5.4.4 Solution of the Equations
5.5 Solution of Ordinary Differential Equations
5.5.1 Taylor’s Series
5.5.2 Picard’s Method
5.5.3 Euler’s Method
5.5.4 Runge–Kutta Methods
5.6 Numerical Solution of Partial Differential Equations
5.7 Exercises
5.8 Questions
References
6 Applications of Models
6.1 Gas–Solid Reaction
6.2 Gasification of Carbon
6.3 Production of Sponge Iron by Rotary Kiln
6.4 Oxygen Jet Momentum in BOF
6.5 Hydrostatic Pressure at the Bottom of Ladle
6.6 Growth and Detachment of Bubbles Nucleating in Liquid Bath
6.7 Continuous Casting (Concast)
6.8 Addition of Slag Powder on Concast
6.9 Production of Duplex Stainless Steel by CONARC
6.9.1 Material Balance
6.9.2 Heat Balance
6.10 Kinetic Model
6.11 Exercises
6.12 Questions
References
Appendix I
(A) Physical Quantities and Their Dimensions
(B) Some Common Mathematical Functions
Appendix II
Equation of Continuity
Appendix III
(A) Equation of Motion (in Terms of τ)
(B) Equation of Motion (Navier–Stokes Equation at Constant ρ and μ) [ { DuDt } = - p +2 u +g ]
Appendix IV
Equations for Diffusion of Heat
Appendix V
(A) Equations for Mass Diffusion (Fick’s Law for Binary Mixture)
(B) General Equations of Mass Diffusion
Appendix VI
Some Dimensionless Numbers