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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 | |