| |

| |

Preface | |

| |

| |

Nomenclature | |

| |

| |

| |

Foundations of Heat Transfer | |

| |

| |

| |

Introductory Remarks | |

| |

| |

| |

Modes of Heat Transfer | |

| |

| |

| |

Continuum Concept | |

| |

| |

| |

Some Definitions and Concepts of Thermodynamics | |

| |

| |

| |

Law of Conservation of Mass | |

| |

| |

| |

First Law of Thermodynamics | |

| |

| |

| |

Second Law of Thermodynamics | |

| |

| |

| |

Temperature Distribution | |

| |

| |

| |

Fourier's Law of Heat Conduction | |

| |

| |

| |

Thermal Conductivity | |

| |

| |

| |

Newton's Cooling Law | |

| |

| |

| |

Stefan-Boltzmann Law of Radiation | |

| |

| |

References | |

| |

| |

Problems | |

| |

| |

| |

General Heat Conduction Equation | |

| |

| |

| |

Introduction | |

| |

| |

| |

General Heat Conduction Equation | |

| |

| |

| |

Initial and Boundary Conditions | |

| |

| |

| |

Initial Condition | |

| |

| |

| |

Boundary Conditions | |

| |

| |

| |

Temperature-Dependent Thermal Conductivity and Kirchhoff Transformation | |

| |

| |

References | |

| |

| |

Problems | |

| |

| |

| |

One-Dimensional Steady-State Heat Conduction | |

| |

| |

| |

Introduction | |

| |

| |

| |

One-Dimensional Steady-State Heat Conduction without Heat Sources | |

| |

| |

| |

Plane Wall | |

| |

| |

| |

Conduction through a Plane Wall from One Fluid to Another | |

| |

| |

| |

Hollow Cylinder | |

| |

| |

| |

Spherical Shells | |

| |

| |

| |

Thermal Resistance Concept | |

| |

| |

| |

Composite Plane Walls | |

| |

| |

| |

Cylindrical Composite Walls | |

| |

| |

| |

Overall Heat Transfer Coefficient | |

| |

| |

| |

Thermal Contact and Scale Resistances | |

| |

| |

| |

Biot Number | |

| |

| |

| |

Critical Thickness of Cylindrical Insulation | |

| |

| |

| |

One-Dimensional Steady-State Heat Conduction with Heat Sources | |

| |

| |

| |

Plane Wall | |

| |

| |

| |

Solid Cylinder | |

| |

| |

| |

Effect of Cladding | |

| |

| |

| |

Temperature-Dependent Thermal Conductivity | |

| |

| |

| |

Space-Dependent Internal Energy Generation | |

| |

| |

| |

Extended Surfaces: Fins and Spines | |

| |

| |

| |

Extended Surfaces with Constant Cross Sections | |

| |

| |

| |

Rectangular Fin of Least Material | |

| |

| |

| |

Performance Factors | |

| |

| |

| |

Heat Transfer from a Finned Wall | |

| |

| |

| |

Limit of Usefulness of Fins | |

| |

| |

| |

Extended Surfaces with Variable Cross Sections | |

| |

| |

References | |

| |

| |

Problems | |

| |

| |

| |

The Sturm-Liouville Theory and Fourier Expansions | |

| |

| |

| |

Introduction | |

| |

| |

| |

Characteristic-Value Problems | |

| |

| |

| |

Orthogonal Functions | |

| |

| |

| |

Sturm-Liouville Problem | |

| |

| |

| |

Generalized Fourier Series | |

| |

| |

| |

Ordinary Fourier Series | |

| |

| |

| |

Fourier Sine Series | |

| |

| |

| |

Fourier Cosine Series | |

| |

| |

| |

Complete Fourier Series | |

| |

| |

| |

Fourier-Bessel Series | |

| |

| |

References | |

| |

| |

Problems | |

| |

| |

| |

Steady-State Two- and Three-Dimensional Heat Conduction: Solutions with Separation of Variables | |

| |

| |

| |

Introduction | |

| |

| |

| |

Two-Dimensional Steady-State Problems in the Rectangular Coordinate System | |

| |

| |

| |

Nonhomogeneity in Boundary Conditions | |

| |

| |

| |

Nonhomogeneity in Differential Equations | |

| |

| |

| |

Two-Dimensional Steady-State Problems in the Cylindrical Coordinate Systems | |

| |

| |

| |

Two-Dimensional Steady-State Problems in (r, [phi]) Variables | |

| |

| |

| |

Steady-State Two-Dimensional Problems in (r, z) Variables | |

| |

| |

| |

Two-Dimensional Steady-State Problems in the Spherical Coordinate Systems | |

| |

| |

| |

Legendre Polynomials | |

| |

| |

| |

Fourier-Legendre Series | |

| |

| |

| |

Solid Sphere | |

| |

| |

| |

Three-Dimensional Steady-State Systems | |

| |

| |

| |

Heat Transfer Rates | |

| |

| |

References | |

| |

| |

Problems | |

| |

| |

| |

Unsteady-State Heat Conduction: Solutions With Separation of Variables | |

| |

| |

| |

Introduction | |

| |

| |

| |

Lumped-Heat-Capacity Systems | |

| |

| |

| |

One-Dimensional Distributed Systems | |

| |

| |

| |

Cooling (or Heating) of a Large Flat Plate | |

| |

| |

| |

Cooling (or Heating) of a Long Solid Cylinder | |

| |

| |

| |

Cooling (or Heating) of a Solid Sphere | |

| |

| |

| |

Multidimensional Systems | |

| |

| |

| |

Cooling (or Heating) of a Long Rectangular Bar | |

| |

| |

| |

Cooling (or Heating) of a Parallelepiped and a Finite Cylinder | |

| |

| |

| |

Semi-Infinite Body | |

| |

| |

| |

Cooling (or Heating) of Semi-Infinite Bars, Cylinders, and Plates | |

| |

| |

| |

Periodic Surface Temperature Change | |

| |

| |

References | |

| |

| |

Problems | |

| |

| |

| |

Solutions with Integral Transforms | |

| |

| |

| |

Introduction | |

| |

| |

| |

Finite Fourier Transforms | |

| |

| |

| |

An Introductory Example | |

| |

| |

| |

Fourier Transforms in the Semi-Infinite and Infinite Regions | |

| |

| |

| |

Unsteady-State Heat Conduction in Rectangular Coordinates | |

| |

| |

| |

A Semi-Infinite Rectangular Strip | |

| |

| |

| |

Infinite Medium | |

| |

| |

| |

Steady-State Two- and Three-Dimensional Problems in Rectangular Coordinates | |

| |

| |

| |

Hankel Transforms | |

| |

| |

| |

Problems in Cylindrical Coordinates | |

| |

| |

| |

Problems in Spherical Coordinate | |

| |

| |

| |

Observations on the Method | |

| |

| |

References | |

| |

| |

Problems | |

| |

| |

| |

Solutions With Laplace Transforms | |

| |

| |

| |

Introduction | |

| |

| |

| |

Definition of the Laplace Transform | |

| |

| |

| |

Introductory Example | |

| |

| |

| |

Some Important Properties of Laplace Transforms | |

| |

| |

| |

The Inverse Laplace Transform | |

| |

| |

| |

Method of Partial Fractions | |

| |

| |

| |

Convolution Theorem | |

| |

| |

| |

Laplace Transforms and Heat Conduction Problems | |

| |

| |

| |

Plane Wall | |

| |

| |

| |

Semi-Infinite Solid | |

| |

| |

| |

Solid Cylinder | |

| |

| |

| |

Solid Sphere | |

| |

| |

References | |

| |

| |

Problems | |

| |

| |

| |

Heat Conduction With Local Heat Sources | |

| |

| |

| |

Introduction | |

| |

| |

| |

The Delta Function | |

| |

| |

| |

Plane Heat Source | |

| |

| |

| |

Cylindrical and Spherical Shell Heat Sources | |

| |

| |

| |

Slab with Distributed and Plane Heat Sources | |

| |

| |

| |

Instantaneous Volumetric Heat Source | |

| |

| |

| |

Plane Heat Source | |

| |

| |

| |

Instantaneous Plane Heat Source | |

| |

| |

| |

Long Solid Cylinder with Cylindrical Shell and Line Heat Sources | |

| |

| |

| |

Cylindrical Shell Heat Source | |

| |

| |

| |

Instantaneous Cylindrical Shell Heat Source | |

| |

| |

| |

Line Heat Source | |

| |

| |

| |

Instantaneous Line Heat Source | |

| |

| |

| |

Solid Sphere with Spherical Shell and Point Heat Sources | |

| |

| |

| |

Spherical Shell Heat Source | |

| |

| |

| |

Instantaneous Spherical Shell Heat Source | |

| |

| |

| |

Point Heat Source | |

| |

| |

| |

Instantaneous Point Heat Source | |

| |

| |

| |

Infinite Region with Line Heat Source | |

| |

| |

| |

Continuous Heat Release | |

| |

| |

| |

Instantaneous Line Heat Source | |

| |

| |

| |

Infinite Region with Point Heat Source | |

| |

| |

| |

Continuous Heat Release | |

| |

| |

| |

Instantaneous Point Heat Source | |

| |

| |

| |

Systems with Moving Heat Sources | |

| |

| |

| |

Quasi-Steady State Condition | |

| |

| |

| |

Moving Plane Heat Source in an Infinite Solid | |

| |

| |

References | |

| |

| |

Problems | |

| |

| |

| |

Further Analytical Methods of Solution | |

| |

| |

| |

Introduction | |

| |

| |

| |

Duhamel's Method | |

| |

| |

| |

The Similarity Method | |

| |

| |

| |

The Integral Method | |

| |

| |

| |

Problems with Temperature-Dependent Thermal Conductivity | |

| |

| |

| |

Nonlinear Boundary Conditions | |

| |

| |

| |

Plane Wall | |

| |

| |

| |

Problems with Cylindrical and Spherical Symmetry | |

| |

| |

| |

Variational Formulation and Solution by the Ritz Method | |

| |

| |

| |

Basics of Variational Calculus | |

| |

| |

| |

Variational Formulation of Heat Conduction Problems | |

| |

| |

| |

Approximate Solutions by the Ritz Method | |

| |

| |

References | |

| |

| |

Problems | |

| |

| |

| |

Heat Conduction Involving Phase Change | |

| |

| |

| |

Introduction | |

| |

| |

| |

Boundary Conditions at a Sharp Moving Interface | |

| |

| |

| |

Continuity of Temperature at the Interface | |

| |

| |

| |

Energy Balance at the Interface | |

| |

| |

| |

A Single-Region Phase-Change Problem | |

| |

| |

| |

Formulation | |

| |

| |

| |

Stefan's Exact Solution | |

| |

| |

| |

Approximate Solution by the Integral Method | |

| |

| |

| |

A Two-Region Phase-Change Problem | |

| |

| |

| |

Formulation | |

| |

| |

| |

Neumann's Exact Solution | |

| |

| |

| |

Solidification Due to a Line Heat Sink in a Large Medium | |

| |

| |

| |

Solidification Due to a Point Heat Sink in a Large Medium | |

| |

| |

| |

Similarity Solution for the Case of q[subscript pt](t) = Q[subscript 0]t[superscript 1/2] | |

| |

| |

| |

Solutions by the Quasi-Steady Approximation | |

| |

| |

| |

Melting of a Slab with Prescribed Surface Temperatures | |

| |

| |

| |

Melting of a Slab with Imposed Surface Heat Flux | |

| |

| |

| |

Melting of a Slab with Convection | |

| |

| |

| |

Outward Melting of a Hollow Cylinder | |

| |

| |

| |

Inward Melting of a Solid Sphere | |

| |

| |

| |

Solidification of Binary Alloys | |

| |

| |

| |

Equilibrium-Phase Diagram | |

| |

| |

| |

Solidification of a Binary Alloy | |

| |

| |

References | |

| |

| |

Problems | |

| |

| |

| |

Numerical Solutions | |

| |

| |

| |

Introduction | |

| |

| |

| |

Finite-Difference Approximation of Derivatives | |

| |

| |

| |

Finite-Difference Formulation of Steady-State Problems in Rectangular Coordinates | |

| |

| |

| |

Finite-Difference Approximation of Boundary Conditions | |

| |

| |

| |

Boundary Exchanging Heat by Convection with a Medium at a Prescribed Temperature | |

| |

| |

| |

Insulated Boundary | |

| |

| |

| |

Irregular Boundaries | |

| |

| |

| |

Solution of Finite-Difference Equations | |

| |

| |

| |

Relaxation Method | |

| |

| |

| |

Matrix Inversion Method | |

| |

| |

| |

Gaussian Elimination Method | |

| |

| |

| |

Finite-Difference Formulation of One-Dimensional, Unsteady-State Problems in Rectangular Coordinates | |

| |

| |

| |

Explicit Method | |

| |

| |

| |

Implicit Method | |

| |

| |

| |

Crank-Nicolson Method | |

| |

| |

| |

Finite-Difference Formulation of Two-Dimensional, Unsteady-State Problems in Rectangular Coordinates | |

| |

| |

| |

Finite-Difference Formulation of Problems in Cylindrical Coordinates | |

| |

| |

| |

Errors in Finite-Difference Solutions | |

| |

| |

| |

Convergence and Stability | |

| |

| |

| |

Graphical Solutions | |

| |

| |

References | |

| |

| |

Problems | |

| |

| |

| |

Thermophysical Properties | |

| |

| |

| |

Bessel Functions | |

| |

| |

| |

Error Function | |

| |

| |

| |

Laplace Transforms | |

| |

| |

| |

Exponential Integral Functions | |

| |

| |

Index | |