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Preface | |
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Nomenclature | |
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Foundations of Heat Transfer | |
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Introductory Remarks | |
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Modes of Heat Transfer | |
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Continuum Concept | |
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Some Definitions and Concepts of Thermodynamics | |
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Law of Conservation of Mass | |
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First Law of Thermodynamics | |
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Second Law of Thermodynamics | |
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Temperature Distribution | |
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Fourier's Law of Heat Conduction | |
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Thermal Conductivity | |
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Newton's Cooling Law | |
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Stefan-Boltzmann Law of Radiation | |
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References | |
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Problems | |
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General Heat Conduction Equation | |
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Introduction | |
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General Heat Conduction Equation | |
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Initial and Boundary Conditions | |
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Initial Condition | |
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Boundary Conditions | |
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Temperature-Dependent Thermal Conductivity and Kirchhoff Transformation | |
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References | |
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Problems | |
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One-Dimensional Steady-State Heat Conduction | |
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Introduction | |
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One-Dimensional Steady-State Heat Conduction without Heat Sources | |
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Plane Wall | |
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Conduction through a Plane Wall from One Fluid to Another | |
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Hollow Cylinder | |
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Spherical Shells | |
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Thermal Resistance Concept | |
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Composite Plane Walls | |
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Cylindrical Composite Walls | |
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Overall Heat Transfer Coefficient | |
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Thermal Contact and Scale Resistances | |
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Biot Number | |
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Critical Thickness of Cylindrical Insulation | |
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One-Dimensional Steady-State Heat Conduction with Heat Sources | |
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Plane Wall | |
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Solid Cylinder | |
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Effect of Cladding | |
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Temperature-Dependent Thermal Conductivity | |
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Space-Dependent Internal Energy Generation | |
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Extended Surfaces: Fins and Spines | |
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Extended Surfaces with Constant Cross Sections | |
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Rectangular Fin of Least Material | |
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Performance Factors | |
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Heat Transfer from a Finned Wall | |
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Limit of Usefulness of Fins | |
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Extended Surfaces with Variable Cross Sections | |
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References | |
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Problems | |
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The Sturm-Liouville Theory and Fourier Expansions | |
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Introduction | |
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Characteristic-Value Problems | |
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Orthogonal Functions | |
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Sturm-Liouville Problem | |
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Generalized Fourier Series | |
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Ordinary Fourier Series | |
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Fourier Sine Series | |
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Fourier Cosine Series | |
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Complete Fourier Series | |
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Fourier-Bessel Series | |
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References | |
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Problems | |
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Steady-State Two- and Three-Dimensional Heat Conduction: Solutions with Separation of Variables | |
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Introduction | |
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Two-Dimensional Steady-State Problems in the Rectangular Coordinate System | |
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Nonhomogeneity in Boundary Conditions | |
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Nonhomogeneity in Differential Equations | |
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Two-Dimensional Steady-State Problems in the Cylindrical Coordinate Systems | |
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Two-Dimensional Steady-State Problems in (r, [phi]) Variables | |
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Steady-State Two-Dimensional Problems in (r, z) Variables | |
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Two-Dimensional Steady-State Problems in the Spherical Coordinate Systems | |
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Legendre Polynomials | |
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Fourier-Legendre Series | |
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Solid Sphere | |
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Three-Dimensional Steady-State Systems | |
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Heat Transfer Rates | |
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References | |
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Problems | |
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Unsteady-State Heat Conduction: Solutions With Separation of Variables | |
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Introduction | |
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Lumped-Heat-Capacity Systems | |
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One-Dimensional Distributed Systems | |
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Cooling (or Heating) of a Large Flat Plate | |
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Cooling (or Heating) of a Long Solid Cylinder | |
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Cooling (or Heating) of a Solid Sphere | |
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Multidimensional Systems | |
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Cooling (or Heating) of a Long Rectangular Bar | |
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Cooling (or Heating) of a Parallelepiped and a Finite Cylinder | |
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Semi-Infinite Body | |
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Cooling (or Heating) of Semi-Infinite Bars, Cylinders, and Plates | |
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Periodic Surface Temperature Change | |
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References | |
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Problems | |
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Solutions with Integral Transforms | |
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Introduction | |
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Finite Fourier Transforms | |
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An Introductory Example | |
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Fourier Transforms in the Semi-Infinite and Infinite Regions | |
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Unsteady-State Heat Conduction in Rectangular Coordinates | |
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A Semi-Infinite Rectangular Strip | |
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Infinite Medium | |
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Steady-State Two- and Three-Dimensional Problems in Rectangular Coordinates | |
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Hankel Transforms | |
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Problems in Cylindrical Coordinates | |
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Problems in Spherical Coordinate | |
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Observations on the Method | |
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References | |
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Problems | |
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Solutions With Laplace Transforms | |
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Introduction | |
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Definition of the Laplace Transform | |
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Introductory Example | |
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Some Important Properties of Laplace Transforms | |
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The Inverse Laplace Transform | |
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Method of Partial Fractions | |
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Convolution Theorem | |
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Laplace Transforms and Heat Conduction Problems | |
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Plane Wall | |
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Semi-Infinite Solid | |
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Solid Cylinder | |
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Solid Sphere | |
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References | |
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Problems | |
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Heat Conduction With Local Heat Sources | |
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Introduction | |
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The Delta Function | |
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Plane Heat Source | |
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Cylindrical and Spherical Shell Heat Sources | |
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Slab with Distributed and Plane Heat Sources | |
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Instantaneous Volumetric Heat Source | |
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Plane Heat Source | |
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Instantaneous Plane Heat Source | |
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Long Solid Cylinder with Cylindrical Shell and Line Heat Sources | |
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Cylindrical Shell Heat Source | |
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Instantaneous Cylindrical Shell Heat Source | |
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Line Heat Source | |
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Instantaneous Line Heat Source | |
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Solid Sphere with Spherical Shell and Point Heat Sources | |
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Spherical Shell Heat Source | |
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Instantaneous Spherical Shell Heat Source | |
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Point Heat Source | |
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Instantaneous Point Heat Source | |
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Infinite Region with Line Heat Source | |
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Continuous Heat Release | |
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Instantaneous Line Heat Source | |
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Infinite Region with Point Heat Source | |
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Continuous Heat Release | |
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Instantaneous Point Heat Source | |
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Systems with Moving Heat Sources | |
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Quasi-Steady State Condition | |
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Moving Plane Heat Source in an Infinite Solid | |
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References | |
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Problems | |
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Further Analytical Methods of Solution | |
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Introduction | |
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Duhamel's Method | |
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The Similarity Method | |
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The Integral Method | |
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Problems with Temperature-Dependent Thermal Conductivity | |
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Nonlinear Boundary Conditions | |
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Plane Wall | |
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Problems with Cylindrical and Spherical Symmetry | |
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Variational Formulation and Solution by the Ritz Method | |
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Basics of Variational Calculus | |
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Variational Formulation of Heat Conduction Problems | |
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Approximate Solutions by the Ritz Method | |
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References | |
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Problems | |
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Heat Conduction Involving Phase Change | |
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Introduction | |
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Boundary Conditions at a Sharp Moving Interface | |
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Continuity of Temperature at the Interface | |
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Energy Balance at the Interface | |
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A Single-Region Phase-Change Problem | |
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Formulation | |
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Stefan's Exact Solution | |
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Approximate Solution by the Integral Method | |
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A Two-Region Phase-Change Problem | |
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Formulation | |
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Neumann's Exact Solution | |
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Solidification Due to a Line Heat Sink in a Large Medium | |
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Solidification Due to a Point Heat Sink in a Large Medium | |
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Similarity Solution for the Case of q[subscript pt](t) = Q[subscript 0]t[superscript 1/2] | |
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Solutions by the Quasi-Steady Approximation | |
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Melting of a Slab with Prescribed Surface Temperatures | |
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Melting of a Slab with Imposed Surface Heat Flux | |
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Melting of a Slab with Convection | |
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Outward Melting of a Hollow Cylinder | |
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Inward Melting of a Solid Sphere | |
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Solidification of Binary Alloys | |
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Equilibrium-Phase Diagram | |
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Solidification of a Binary Alloy | |
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References | |
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Problems | |
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Numerical Solutions | |
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Introduction | |
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Finite-Difference Approximation of Derivatives | |
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Finite-Difference Formulation of Steady-State Problems in Rectangular Coordinates | |
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Finite-Difference Approximation of Boundary Conditions | |
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Boundary Exchanging Heat by Convection with a Medium at a Prescribed Temperature | |
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Insulated Boundary | |
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Irregular Boundaries | |
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Solution of Finite-Difference Equations | |
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Relaxation Method | |
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Matrix Inversion Method | |
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Gaussian Elimination Method | |
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Finite-Difference Formulation of One-Dimensional, Unsteady-State Problems in Rectangular Coordinates | |
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Explicit Method | |
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Implicit Method | |
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Crank-Nicolson Method | |
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Finite-Difference Formulation of Two-Dimensional, Unsteady-State Problems in Rectangular Coordinates | |
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Finite-Difference Formulation of Problems in Cylindrical Coordinates | |
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Errors in Finite-Difference Solutions | |
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Convergence and Stability | |
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Graphical Solutions | |
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References | |
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Problems | |
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Thermophysical Properties | |
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Bessel Functions | |
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Error Function | |
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Laplace Transforms | |
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Exponential Integral Functions | |
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Index | |