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A B C D E F G H I J K L M N O P Q R S
Saddle supports, for heat exchangers, Safety factors, Safety, of heat exchangers: Salicyl aldehyde: Salts, heat transfer, as heat transfer media, Sand roughness, equivalent, Santotherm, heat transfer media, Sastri and Rao correlation for surface tension, Saturated boiling: Saturated density: Saturated fluids, tables of physical properties, Saturation pressure, Saturation temperature, Saunders, E A D Sauer, H J Jr, Scale formation in heat exchangers, Scaling approximations, in nonisothermal gas radiation, Scattering bed models, for radiative heat transfer from surfaces, Scattering, interaction phenomena with, Scattering coefficient, Schack wide-band model, for gas radiation properties, Schick and Prausnitz method, for critical volume of mixtures, Schlunder, E U Schmidt, F W Schmidt correlation, for heat transfer in in-line banks of high fin tubes, Schmidt number, Schneider, G E, Schrock and Grossman correlations, for forced convective heat transfer in two-phase flow, Schunk, M Schwier, K, Scraped surfaces: Scaling devices, in shell-and-tube heat exchangers, Seawater physical properties, Seider-Tate equation, for heat transfer in heat exchangers, Selection of heat transfer equipment: Semiconductors, thermal conductivity, Separated flow model: Separation, exergy analysis for, Separators, for use in association with evaporators, Series solutions, for one-dimensional transient conduction, Serrated fins, in plate fin heat exchangers, Shah correlation for boiling, Shah correlation, for boiling in horizontal tubes, Shape factor, in radiative heat transfer between diffuse surfaces, Shear flow, of non-Newtonian fluids, Shear free flow, of non-Newtonian fluids, Shear rate, in fluid, Shear stress: Sheffield, J W, Shelf dryer, Shell-and-tube heat exchanger: Shell-to-baffle clearance, in shell-and-tube heat exchangers, Shells, for shell-and-tube heat exchangers: Sherwood number Shipes, K V, Short-tube vertical evaporator, Sigma phase embrittlement, of stainless steels, Silicate scales, in heat exchangers, Silicone oils, as heat transfer media, physical properties of, Silver method, for calculation of multicomponent condensation, Similarity theory, Simonis, V, Single-phase fluid flow: Single stage flash evaporation (SSF): Singularities, two-phase gas-liquid pressure drop across, Sink, in radiation: Skid-mounted units, specification of, Skin friction coefficient, Skrinska, A, Slab: Sleeves, internal, for expansion bellows, Slot: Slug flow: Slugging, in fluidized beds, Smith, A A, Smith, R, Smith, R A Smith, O, Snell's law, in radiation, Software, for code design, Solar absorber, Solar reflector, Soldered fins, in double pipe exchangers, Solid fuels, properties of, Solids circulation, in fluidized beds, Solid-gas flow: Solid-liquid flow: Solidification: Solids: Solids circulation, in fluidized beds, Soot blowing, Sound velocity: Source, in radiation: Spacers, in shell-and-tube heat exchangers, Spalding, D B, Sparging: Specific enthalpy, Specific entropy: Specific heat capacity, Specific internal energy, Specific volume: Specification of heat exchangers, Spectral absorptivity: Spectral emissivity, in gases, Specular surface, Specular-walled passages, radiative heat transfer in, Spheres: Spherical coordinates, for finite difference equations for conduction, Spherical shells: Spheroids (oblate and prolate), free convective heat transfer from, Spine fins: Spiral heat exchanger: Spirally fluted tubes: Sponge rubber balls, in fouling mitigation, Spray dryers, Sprays, in heat exchangers, Square ducts: Stable equilibrium, of vapor and liquid, Staggered tube banks: Stainless steels, Stanton number Startup: State diagram, for fluidized beds, Static mixers, in heat exchangers, Statically stable foams, Steam, dropwise condensation of, Steam tables, Steam turbine exhaust condensers, Steels, as material of construction, Stefan-Boltzmann constant, Stefan's law, for blackbody radiation, Stegmaier, W, Steiner and Taborek correlation, for forced convective boiling, Stephan and Korner correlation, for boiling of binary mixtures, Stiffeners, PD5500 code guidelines for, Stiffeners, against external pressure, EN13445 guidance on, Stirred beds, heat transfer to, Stirred reactor model, for furnaces, Stone's strongly implicit method, Straight fins (longitudinal fins): Stratified gas-liquid flow: Stratified liquid-liquid-gas flow: Steam analysis methods, for shell-side heat transfer and pressure drop in shell-and-tube heat exchangers, Stress, compressive, in heat exchanger tubes, Stress corrosion cracking, of stainless steels, Stress equation models, for turbulent boundary layers, Stress-strain curve, for solids, Stress tensor: Stresses: Strip baffles, in tube bundles with longitudinal flow, Strouhal number, Subchannel analysis, for critical heat flux in rod bundles, Subcooled boiling: Subcooling: Sublayer, viscous, Submerged combustion, Successive over-under relaxation method for solution of implicit equations, Suction: Suction line exchangers in refrigeration, Sulfur: Sulfur compounds (organic): Sulfur dioxide: Sulfur hexafluoride: Sulfur trioxide: Supercritical fluids: Superficial velocity, in multiphase flow, Superheated gases: Superheated liquid, in metastable state, Superheated vapor, condensation of, on vertical surface, Supersaturation, as cause of fogging in condensers: Suppression of nucleate boiling, Surface catalysis, in augmentation of heat transfer, Surface condensers, Surface finish: Surface, hydraulically smooth, Surface material, effect on fouling, Surface models, in radiative heat transfer, Surface modification for drag reduction, Surface temperature, effect on fouling, Surface tension: Surfactants, in drag reduction, Suspension, radiation interaction phenomena in, Sutherland formula, for viscosity variation with temperature, Sutterby fluid (non-Newtonian), free convective heat transfer to, Swirling flow, in augmentation of heat transfer, Synthetic heat transfer media, Synthetic mixture heat transfer media,
T U V W X Y Z

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

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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