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A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Ideal gas: Ilexan, heat transfer medium, Illingworth, A, Imbedded fins, Immersed bodies: Immersed tubes, in fluidized beds, heat transfer to, Immiscible liquids, condensation of vapors producing Impairment of heat transfer in combined free and forced convection in a vertical pipe, Imperfectly diffuse surfaces: Impingement damage in heat exchangers, Impingement plate: Impingement protection, in shell-and-tube heat exchangers, Impinging jets: Implicit equations, solution of
Finite-Difference Methods for Conduction successive over-under relaxation (SOR), Gauss-Seidel method, Stone's strongly implicit method,
Inclined enclosures, free convective heat transfer in, Inclined flow, effect of on heat transfer to cylinders, Inclined pipes: Inclined surfaces, free convective heat transfer from, Inconel, spectral characteristics of reflectance from oxidized surface of, Induced flow instabilities, in augmentation of heat transfer, Injection: Inlet effects in shell-and-tube heat exchangers, In-line tube banks: Inorganic compounds, solutions of, as heat transfer media, Inorganic substances: Instability, parallel channel, in condensers, Insulators, thermal conductivity of, Integral condensation: Integral finned tubes: Interaction coefficients in heat exchangers, Interaction parameters for binary systems, tables, Interfacial friction, in three-phase (liquid-liquid-gas) stratified flows, Interfacial resistance, in condensation, Interfacial roughness, relationships for, in annular gas-liquid flow, Interfacial shear stress, effect on filmwise condensation, on vertical surface, Intergrannular corrosion, of Intermating troughs, as corrugation design in plate heat exchangers, Intermittent flows: Internal heat sources, temperature distribution in bodies with, Internal heat transfer coefficient, use in transient conduction calculations, Internal reboilers (in distillation columns), characteristics advantages and disadvantages of, Internally finned tubes: International codes for pressure vessels, Interpenetrating continua (as representation of heat exchangers): Intertube velocity, in tube banks, Inviscid flow, compressible, with heat addition, Iodine: Iodobenzene: Iodoethane: Iodomethane: ISO codes for mechanical design of heat exchangers, Isobutane: Isobutanol: Isobutylamine: Isobutylformate: Isobutyric acid: Isoparaffins: Isopentane: Isopentanol: Isopropanol: Isopropylacetate: Isopropylamine: Isopropylbenzene: Isopropylcyclohexane: Isothermal flow, compressible, in ducts, Isothermal gas, radiation heat transfer to walls from, Isotropic materials, elastic properties, Isotropic scattering, Italy, guide to national practice for heat exchanger mechanical design,

Index

HEDH
A B C D E F G H I
Ideal gas: Ilexan, heat transfer medium, Illingworth, A, Imbedded fins, Immersed bodies: Immersed tubes, in fluidized beds, heat transfer to, Immiscible liquids, condensation of vapors producing Impairment of heat transfer in combined free and forced convection in a vertical pipe, Imperfectly diffuse surfaces: Impingement damage in heat exchangers, Impingement plate: Impingement protection, in shell-and-tube heat exchangers, Impinging jets: Implicit equations, solution of
Finite-Difference Methods for Conduction successive over-under relaxation (SOR), Gauss-Seidel method, Stone's strongly implicit method,
Inclined enclosures, free convective heat transfer in, Inclined flow, effect of on heat transfer to cylinders, Inclined pipes: Inclined surfaces, free convective heat transfer from, Inconel, spectral characteristics of reflectance from oxidized surface of, Induced flow instabilities, in augmentation of heat transfer, Injection: Inlet effects in shell-and-tube heat exchangers, In-line tube banks: Inorganic compounds, solutions of, as heat transfer media, Inorganic substances: Instability, parallel channel, in condensers, Insulators, thermal conductivity of, Integral condensation: Integral finned tubes: Interaction coefficients in heat exchangers, Interaction parameters for binary systems, tables, Interfacial friction, in three-phase (liquid-liquid-gas) stratified flows, Interfacial resistance, in condensation, Interfacial roughness, relationships for, in annular gas-liquid flow, Interfacial shear stress, effect on filmwise condensation, on vertical surface, Intergrannular corrosion, of Intermating troughs, as corrugation design in plate heat exchangers, Intermittent flows: Internal heat sources, temperature distribution in bodies with, Internal heat transfer coefficient, use in transient conduction calculations, Internal reboilers (in distillation columns), characteristics advantages and disadvantages of, Internally finned tubes: International codes for pressure vessels, Interpenetrating continua (as representation of heat exchangers): Intertube velocity, in tube banks, Inviscid flow, compressible, with heat addition, Iodine: Iodobenzene: Iodoethane: Iodomethane: ISO codes for mechanical design of heat exchangers, Isobutane: Isobutanol: Isobutylamine: Isobutylformate: Isobutyric acid: Isoparaffins: Isopentane: Isopentanol: Isopropanol: Isopropylacetate: Isopropylamine: Isopropylbenzene: Isopropylcyclohexane: Isothermal flow, compressible, in ducts, Isothermal gas, radiation heat transfer to walls from, Isotropic materials, elastic properties, Isotropic scattering, Italy, guide to national practice for heat exchanger mechanical design,
J K L M N O P Q R S T U V W X Y Z
I Implicit equations, solution of
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Finite-Difference Methods for Conduction

DOI 10.1615/hedhme.a.000165

2.4.7 Finite-Difference Methods for Conduction

F. W. Schmidt

A. Introduction

The widespread use of numerical techniques for the solution of heat conduction problems is very well documented in the technical literature. A number of factors have contributed to the popularity of numerical techniques. They are capable of handling complex geometrical configurations, composite media, both nonlinear and linear boundary conditions, and variable termophysical properties. Transient as well as steady-state conduction problems can be analyzed. Perhaps the most important factor, however, has been the rapid increase in the availability of digital computers to practicing engineers, enabling them easily to apply numerical techniques for the solution of everyday engineering problems.

Numerical techniques, as applied to conduction heat transfer, can be classified as either finite-difference or finite-element methods. This section will deal only with finite-difference methods; Section 166 concentrates on finite-element methods.

A general discussion of finite-difference methods and their use for flow predictions has been presented in Section 1.4. This section will concentrate on the application of these methods to conduction problems, in which the geoemtrical configuration of the region is of considerable importance. Although a number of generalized conduction programs are commercially available, the practicing engineer can easily employ the techniques to be described to obtain satisfactory accuracy with computational power as small as that provided by a desktop personal computer (PC).

The steps used to obtain a finite-difference solution can be categorized as follows:

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