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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
Damage, sources of heat exchangers Damkohler number: Damping: Davis and Anderson criterion, for onset of nucleate boiling, Decal, heat transfer medium, Decane: 1-Decanol: 1-Decene: Degradation temperature, of polymers, Demisters, wire mesh, for multistage flash evaporators, Dengler and Addoms correlation, for forced convective heat transfer in two-phase flow, Density: Deposition of droplets in annular flow Deposition in fouling, Desalination plants: Desuperheaters for use in association with evaporators, Developing flow in ducts: Dew-poin corrosion, Diathermanous fluid, 1,1-Dibromoethane: Dibromomethane: 1,2-Dibromotetrafluoroethane (Refrigerant 114B2): Dibutylamine: Dibutyl ether: Dichloroacetic acid: o-Dichlorobenzene: Dichlorodifluoromethane (see Refrigerant 12) 1,1-Dichloroethane (Refrigerant 150a): 1,2-Dichloroethane (Refrigerant 150): 1,1-Dichloroethylene: cis-1,2-Dichloroethylene: trans-1,2-Dichloroethylene: Dichlorofluoromethane (see Refrigerant 21) Dichloromethane (Refrigerant 30): 1,2-Dichlorotetrafluoroethane (Refrigerant 114) 1,2,3-Dichlorotrifluoroethane (Refrigerant 123) Dielectric constant, of water, Diethylamine: n,n-Diethylaniline: Diethylene glycol: Diethyl ether: Diethyl ketone: Diethylsulfide: Differential condensation: Differential formulations for nonisothermal gas radiation, Differential resistance term in heat exchanger design, Differential vector operators in heat conduction, Diffraction models for radiative heat transfer from surfaces, Diffuse surfaces, radiative heat transfer between, Diffuse wall passages, radiative heat transfer in, Diffusers, single-phase flow and pressure drop in, Diffusion, in multi-component condensation, n,n-Diffusion coefficients: 1,1-Difluoroethane (Refrigerant 152a): Difluoromethane (Refrigerant 32): Diiodomethane: Diisobutylamine: Diisopropylamine: Diisopropylether: Dimensional analysis: Dimensionless groups: Dimethylacetylene: Dimethylamine: Dimethylaniline: 2,2-Dimethylbutane: 2,3-Dimethylbutane: 1,1-Dimethylcyclopentane: Dimethylether: Dimethylketone: 2,2-Dimethylpropane (neopentane): Dimethylsulfide: Dimpled surfaces, heat exchangers with, 1,4-Dioxane: Diphenyl: Diphenylamine: Diphenylether: Diphenylmethane: Dipropyl ether: Diisopropyl ether: Dipropyl ketone: Direct contact heat exchangers Direct contact heat transfer, Direct numerical simulation, of turbulence, Dirichlet boundary condition, finite difference method, Dished heads: Discretization in numerical analysis: Disk-and-doughnut baffled heat exchangers, Disks, free convective heat transfer from inclined, Dispersants, for fouling control, Dispersed flow (liquid-liquid), Dissipation of turbulent energy, Distillation: Distribution: Dittus-Boelter equation, for single-phase forced convective heat transfer, Dividing flow, loss coefficients in, Dodecane: 1-Dodecene: Donohue method, for shell-side heat transfer in shell-and-tube heat exchangers, Double-pipe heat exchangers: Double segmental baffled heat exchangers, Downward facing surfaces, free convective heat transfer from, Downward flow in vertical tubes, flow patterns in gas/liquid, Dowtherm A: Dowtherm J: Dowtherms, as heat transfer media, Drag coefficient: Drag force: Drag reduction, Drainage, of condensate, Dreitser, G, Drift flux model for two-phase flows, Drogemuller, P, Droplets: Dropwise condensation Dry wall desuperheating (in condensation), Dryers: Drying loft, Drying rates, prediction of, Dryout: Ducts, single-phase fluid flow and pressure drop in, Duplex stainless steels, Durand correlation for heterogeneous conveyance in solid/liquid flow, Dynamically stable foam, Dyphyl, heat transfer media, Dzyubenko, B,

Index

HEDH
A B C D
Damage, sources of heat exchangers Damkohler number: Damping: Davis and Anderson criterion, for onset of nucleate boiling, Decal, heat transfer medium, Decane: 1-Decanol: 1-Decene: Degradation temperature, of polymers, Demisters, wire mesh, for multistage flash evaporators, Dengler and Addoms correlation, for forced convective heat transfer in two-phase flow, Density: Deposition of droplets in annular flow Deposition in fouling, Desalination plants: Desuperheaters for use in association with evaporators, Developing flow in ducts: Dew-poin corrosion, Diathermanous fluid, 1,1-Dibromoethane: Dibromomethane: 1,2-Dibromotetrafluoroethane (Refrigerant 114B2): Dibutylamine: Dibutyl ether: Dichloroacetic acid: o-Dichlorobenzene: Dichlorodifluoromethane (see Refrigerant 12) 1,1-Dichloroethane (Refrigerant 150a): 1,2-Dichloroethane (Refrigerant 150): 1,1-Dichloroethylene: cis-1,2-Dichloroethylene: trans-1,2-Dichloroethylene: Dichlorofluoromethane (see Refrigerant 21) Dichloromethane (Refrigerant 30): 1,2-Dichlorotetrafluoroethane (Refrigerant 114) 1,2,3-Dichlorotrifluoroethane (Refrigerant 123) Dielectric constant, of water, Diethylamine: n,n-Diethylaniline: Diethylene glycol: Diethyl ether: Diethyl ketone: Diethylsulfide: Differential condensation: Differential formulations for nonisothermal gas radiation, Differential resistance term in heat exchanger design, Differential vector operators in heat conduction, Diffraction models for radiative heat transfer from surfaces, Diffuse surfaces, radiative heat transfer between, Diffuse wall passages, radiative heat transfer in, Diffusers, single-phase flow and pressure drop in, Diffusion, in multi-component condensation, n,n-Diffusion coefficients: 1,1-Difluoroethane (Refrigerant 152a): Difluoromethane (Refrigerant 32): Diiodomethane: Diisobutylamine: Diisopropylamine: Diisopropylether: Dimensional analysis: Dimensionless groups: Dimethylacetylene: Dimethylamine: Dimethylaniline: 2,2-Dimethylbutane: 2,3-Dimethylbutane: 1,1-Dimethylcyclopentane: Dimethylether: Dimethylketone: 2,2-Dimethylpropane (neopentane): Dimethylsulfide: Dimpled surfaces, heat exchangers with, 1,4-Dioxane: Diphenyl: Diphenylamine: Diphenylether: Diphenylmethane: Dipropyl ether: Diisopropyl ether: Dipropyl ketone: Direct contact heat exchangers Direct contact heat transfer, Direct numerical simulation, of turbulence, Dirichlet boundary condition, finite difference method, Dished heads: Discretization in numerical analysis: Disk-and-doughnut baffled heat exchangers, Disks, free convective heat transfer from inclined, Dispersants, for fouling control, Dispersed flow (liquid-liquid), Dissipation of turbulent energy, Distillation: Distribution: Dittus-Boelter equation, for single-phase forced convective heat transfer, Dividing flow, loss coefficients in, Dodecane: 1-Dodecene: Donohue method, for shell-side heat transfer in shell-and-tube heat exchangers, Double-pipe heat exchangers: Double segmental baffled heat exchangers, Downward facing surfaces, free convective heat transfer from, Downward flow in vertical tubes, flow patterns in gas/liquid, Dowtherm A: Dowtherm J: Dowtherms, as heat transfer media, Drag coefficient: Drag force: Drag reduction, Drainage, of condensate, Dreitser, G, Drift flux model for two-phase flows, Drogemuller, P, Droplets: Dropwise condensation Dry wall desuperheating (in condensation), Dryers: Drying loft, Drying rates, prediction of, Dryout: Ducts, single-phase fluid flow and pressure drop in, Duplex stainless steels, Durand correlation for heterogeneous conveyance in solid/liquid flow, Dynamically stable foam, Dyphyl, heat transfer media, Dzyubenko, B,
E F G H I J K L M N O P Q R S T U V W X Y Z

Finite-Difference Methods for Conduction

DOI 10.1615/hedhme.a.000165

2.4.7 Finite-Difference Methods for Conduction

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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