165--Finite-Difference Methods for Conduction

doi:10.1615/hedhme.a.000165

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Absorbing media, interaction phenomena in, Absorption of thermal radiation: Absorption coefficient, Absorption spectra in gases, Absorptivity: Acentric factor: Acetaldehyde: Acetic acid: Acetic anhydride: Acetone: Acetonitrile: Acetophenone: Acetylene: Acetylenes Ackerman correction factor in condensation, Acoustic methods, for fouling mitigation, Acoustic vibration of heat exchangers, Acrolein: Acrylic acid: Active systems for augmentation of heat transfer: Additives: Adiabatic flows, compressible, in duct, Admiralty brass, Advanced models for furnaces, Agitated beds, heat transfer to, Agitated vessels, Ahmad scaling method for critical heat flux in flow boiling of nonaqueous fluids, Air: Air-activated gravity conveyor, Air-cooled heat exchangers: Air preheaters, fouling in, Albedo for single scatter in radiation, Alcohols: Aldehydes: Aldred, D L, Allyl alcohol: Allyl chloride (-chloropropane) Alternating direction (ADR) method, for solution of implicit finite difference equations,

Finite-Difference Methods for Conduction program for,

Aluminum, spectral characteristics of anodized surfaces, Aluminum alloys, thermal and mechanical properties, Aluminium brass, Ambrose-Walton corresponding states method, for vapour pressure, Amides: Amines: Ammonia: tert-Amyl alcohol: Analogy between heat and mass and momentum transfer Analytical solution of groups, for calculation of thermodynamic Anelasticity, Angled tubes, use in increasing flooding rate in reflux condensation, Aniline: Anisotropy of elastic properties, Annular distributor in shell-and-tube heat exchangers, Annular ducts: Annular (radial) fins, efficiency Annular flow (gas-liquid): Annular flow (liquid-liquid), Annular flow (liquid-liquid-gas), Anti-foulants, Antoine equation, for vapour pressure, Aqueous solutions, as heat transfer media, Arc welding of tubes into tube sheets: Archimedes number, Area of tube outside surface in shell-and-tube heat exchangers: Argon: Arithmetic mean temperature difference, definition, Armstrong, Robert C Aromatics: ASME VIII code, for mechanical design of shell-and-tube heat exchangers: Assisted convection: Attachment, of fouling layers, Augmentation of heat transfer Austenitic stainless steels, Average phase velocity in multiphase flows, Axial flow reboilers, Axial wire attachments, for augmentation of condensation, Azeotropes, condensation of

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Absorbing media, interaction phenomena in, Absorption of thermal radiation: Absorption coefficient, Absorption spectra in gases, Absorptivity: Acentric factor: Acetaldehyde: Acetic acid: Acetic anhydride: Acetone: Acetonitrile: Acetophenone: Acetylene: Acetylenes Ackerman correction factor in condensation, Acoustic methods, for fouling mitigation, Acoustic vibration of heat exchangers, Acrolein: Acrylic acid: Active systems for augmentation of heat transfer: Additives: Adiabatic flows, compressible, in duct, Admiralty brass, Advanced models for furnaces, Agitated beds, heat transfer to, Agitated vessels, Ahmad scaling method for critical heat flux in flow boiling of nonaqueous fluids, Air: Air-activated gravity conveyor, Air-cooled heat exchangers: Air preheaters, fouling in, Albedo for single scatter in radiation, Alcohols: Aldehydes: Aldred, D L, Allyl alcohol: Allyl chloride (-chloropropane) Alternating direction (ADR) method, for solution of implicit finite difference equations,

Finite-Difference Methods for Conduction program for,

Aluminum, spectral characteristics of anodized surfaces, Aluminum alloys, thermal and mechanical properties, Aluminium brass, Ambrose-Walton corresponding states method, for vapour pressure, Amides: Amines: Ammonia: tert-Amyl alcohol: Analogy between heat and mass and momentum transfer Analytical solution of groups, for calculation of thermodynamic Anelasticity, Angled tubes, use in increasing flooding rate in reflux condensation, Aniline: Anisotropy of elastic properties, Annular distributor in shell-and-tube heat exchangers, Annular ducts: Annular (radial) fins, efficiency Annular flow (gas-liquid): Annular flow (liquid-liquid), Annular flow (liquid-liquid-gas), Anti-foulants, Antoine equation, for vapour pressure, Aqueous solutions, as heat transfer media, Arc welding of tubes into tube sheets: Archimedes number, Area of tube outside surface in shell-and-tube heat exchangers: Argon: Arithmetic mean temperature difference, definition, Armstrong, Robert C Aromatics: ASME VIII code, for mechanical design of shell-and-tube heat exchangers: Assisted convection: Attachment, of fouling layers, Augmentation of heat transfer Austenitic stainless steels, Average phase velocity in multiphase flows, Axial flow reboilers, Axial wire attachments, for augmentation of condensation, Azeotropes, condensation 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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