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Rabas and Taborek correlation, for heat transfer in banks of low fin tubes, Rackett equation (modified) for liquid density Radiation: Radiation shields, in radiation heat transfer, Radiation source analysis, Radiative heat transfer: Radiators, automotive, construction, Radiometers, application in gas radiation property measurement, Radiosity, Stephan's law for, Radiosity-irradiation formulations in radiative heat transfer, Rankine cycle in refrigeration, Rao, B K Raoult's law for partial pressure, Rating of heat exchangers, Rayleigh instability, in free convection, Rayleigh number Reay, D Reboilers: Reciprocal mode integrating sphere, for reflection and transmission measurements in radiation, Rectangles: Rectangular ducts: Rectangular enclosures, free convective heat transfer in: Rectangular fins, for plate fin exchangers Reduced pressure, correlations for pool boiling using, Reference temperature: Refinery processes, fouling in, Reflection, of thermal radiation, from solid surfaces: Reflectivity, of solid surfaces, Reflectometer, heated cavity, Reflux condensers, Refractories, density of, Refractory surfaces, Refrigerants: Refrigerant 11 (Trichlorofluoromethane): Refrigerant 12 (Dichlorodifluoromethane): Refrigerant 13 (Chlorotrifluoromethane): Refrigerant 21 (Dichlorofluoromethane): Refrigerant 22 (Chlorodifluoromethane): Refrigerant 116: Refrigerant plant, entropy generation in, Refrigeration, heat transfer in, Regenerators and thermal energy storage, Regimes of heat transfer, in ducts, single phase flow, Reidel method, for predicting enthalpy of vaporisation, Reinforcing rings, for expansion bellows, Relaminarization, of turbulent flow, Reichenberg method, for effect of pressure on gas viscosity, Relief system design for shell-and-tube heat exchangers with tube side failure, Removal of fouling deposits: Renewable fuels, properties of, Renotherm, heat transfer medium, Repair, of expansion bellows, Residence times, in dryers: Resistance network analysis, Resistance (thermal) due to fouling: Reversible (minimum) work, in Reynolds number, Reynolds stress models, for turbulence, Rheologically complex materials, properties of: Rheological properties of drag reducing agents Rheology, shear flow experiments used in, Rhine, J M, Ribatski, G, Riblets for drag reduction, Richardson number, Richie, J M, Ring cells, in free convection, RODbaffles, in tube bundles with longitudinal flow, Rod bundles: Rohsenow correlation, for nucleate boiling, Roll cells, in free convection, Roller expansion, of tubes into tube sheets, Rose, J W, Rossby number, Rotary dryer, Rotating drums, heat transfer to particle bed in, Rotating surface, in an annular duct Rotation, as device for heat transfer augmentation, Roughness, surface: Rough walled passages, radiative heat transfer down,
Radiation Transfer Between Specular and Imperfectly Diffuse Surfaces
Rubber (sponge) balls, in fouling mitigation, Ryznar index for water quality,

Index

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A B C D E F G H I J K L M N O P Q R
Rabas and Taborek correlation, for heat transfer in banks of low fin tubes, Rackett equation (modified) for liquid density Radiation: Radiation shields, in radiation heat transfer, Radiation source analysis, Radiative heat transfer: Radiators, automotive, construction, Radiometers, application in gas radiation property measurement, Radiosity, Stephan's law for, Radiosity-irradiation formulations in radiative heat transfer, Rankine cycle in refrigeration, Rao, B K Raoult's law for partial pressure, Rating of heat exchangers, Rayleigh instability, in free convection, Rayleigh number Reay, D Reboilers: Reciprocal mode integrating sphere, for reflection and transmission measurements in radiation, Rectangles: Rectangular ducts: Rectangular enclosures, free convective heat transfer in: Rectangular fins, for plate fin exchangers Reduced pressure, correlations for pool boiling using, Reference temperature: Refinery processes, fouling in, Reflection, of thermal radiation, from solid surfaces: Reflectivity, of solid surfaces, Reflectometer, heated cavity, Reflux condensers, Refractories, density of, Refractory surfaces, Refrigerants: Refrigerant 11 (Trichlorofluoromethane): Refrigerant 12 (Dichlorodifluoromethane): Refrigerant 13 (Chlorotrifluoromethane): Refrigerant 21 (Dichlorofluoromethane): Refrigerant 22 (Chlorodifluoromethane): Refrigerant 116: Refrigerant plant, entropy generation in, Refrigeration, heat transfer in, Regenerators and thermal energy storage, Regimes of heat transfer, in ducts, single phase flow, Reidel method, for predicting enthalpy of vaporisation, Reinforcing rings, for expansion bellows, Relaminarization, of turbulent flow, Reichenberg method, for effect of pressure on gas viscosity, Relief system design for shell-and-tube heat exchangers with tube side failure, Removal of fouling deposits: Renewable fuels, properties of, Renotherm, heat transfer medium, Repair, of expansion bellows, Residence times, in dryers: Resistance network analysis, Resistance (thermal) due to fouling: Reversible (minimum) work, in Reynolds number, Reynolds stress models, for turbulence, Rheologically complex materials, properties of: Rheological properties of drag reducing agents Rheology, shear flow experiments used in, Rhine, J M, Ribatski, G, Riblets for drag reduction, Richardson number, Richie, J M, Ring cells, in free convection, RODbaffles, in tube bundles with longitudinal flow, Rod bundles: Rohsenow correlation, for nucleate boiling, Roll cells, in free convection, Roller expansion, of tubes into tube sheets, Rose, J W, Rossby number, Rotary dryer, Rotating drums, heat transfer to particle bed in, Rotating surface, in an annular duct Rotation, as device for heat transfer augmentation, Roughness, surface: Rough walled passages, radiative heat transfer down,
Radiation Transfer Between Specular and Imperfectly Diffuse Surfaces
Rubber (sponge) balls, in fouling mitigation, Ryznar index for water quality,
S T U V W X Y Z
R Rough walled passages, radiative heat transfer down,
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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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