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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,
Radiation Transfer Between Specular and Imperfectly Diffuse 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,
Radiation Transfer Between Specular and Imperfectly Diffuse 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
D Diffraction models for radiative heat transfer from surfaces,
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Radiation Transfer Between Specular and Imperfectly Diffuse Surfaces

DOI 10.1615/hedhme.a.000207

2.9 HEAT TRANSFER BY RADIATION
2.9.4 Radiation transfer between specular and imperfectly diffuse surfaces

D.K. Edwards

A. Specular and imperfectly diffuse surfaces

The concept of a perfectly diffuse surface was an artifice introduced to simplify formal mathematical analysis of radiant transfer. The concept is widely used in engineering design and analysis for its convenience, and, surprisingly, the answers so obtained are found in many instances to be remarkably close to the answers found with more realistic analytical models. There are situations — for example, in transmission through long passages with specular side walls — where the assumption of perfectly diffuse reflection will lead to serious error, however. Thus the designer or analyst needs to be able to carry out calculations when one or more surfaces are not perfectly diffuse.

Perfectly diffuse reflection is where the bidirectional reflectance is a constant independent of all four angles, the two angles of incidence and the two of emergence. The antithesis of perfectly diffuse reflection is specular reflection, where the bidirectional reflectance is identically zero for all directions of emergence except the specular angle where it has an integrable singularity. Imperfectly diffuse is the term usually used to denote that the bidirectional reflectance is nonzero but not constant with angles of emergence. Mixed specular diffuse reflection occurs when there is a specular component, for example, from the smooth surface of the binder of a glossy enamel paint, and a (perfectly or imperfectly) diffuse component, for example, from the underlying particles of pigment of such a glossy enamel.

B. The mirror-image concept

The mirror-image concept was introduced formally into thermal radiation transfer analysis by Eckert, Sparrow, and co-workers (Eckert and Sparrow,1961; Sparrow et al., 1964). The concept is useful primarily when the enclosure in question contains only a few plane specular surfaces arranged so that the number of multiple specular reflections is either limited or forms an easily summed chain. The concept is based on the fact that a ray coming from an element of diffuse surface i and reflected by mirror m to an element of diffuse surface j can be regarded as an uninterrupted straight line from i to the mirror image of j. Thus the shape factor of Equation 206.5 can be applied between surface i and the mirror image of j in calculating the transfer between i and j via m. The image of j as seen in m is denoted j(m). The mirror-image shape factor is then written Fi–j(m).

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