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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
McNaught, J M, Macdonald equation, for fixed-bed pressure drop, Mach number, Macleod-Sugden method for surface tension Macrolayer consumption model for critical heat flux in pool boiling, Maddox, R N Magnetic fields, effect on properties of rheologically complex materials, Magnetic devices, for fouling mitigation, Magnetohydrodynamcs, inaugmentation of heat transfer in microfluidic systems, Margarine manufacture, crystallization of edible oils and fats in, scraped surface heat exchangers for, Marlotherm, heat transfer media, Martensitic stainless steels, Martin, H Martinelli and Boelter equations for combined free and forced convection, Martinelli and Nelson correlations: Mass absorption coefficient, Mass extinction coefficient, Mass fraction, in multicomponent mixtures, Mass scattering coefficient, Mass transfer: Mass transfer coefficient: Materials of construction, for heat exchangers, Low temperature operation, ASME VIII code guidelines for, Matovosian, Robert, Matrix inversion techniques, in radiative heat transfer, Maximum drag reduction Maximum velocities (in shell-and-tube heat exchangers) Maxwell model, for non-Newtonian fluid, Maxwell-Stefan equations, for multicomponent diffusion, Maxwell's equations, for electromagnetic radiation, Mean beam length concept, in radiative heat transfer: Mean phase content, Mean temperature difference: Measurement of fouling resistance, Mechanical design of heat exchangers: Mechanical draft cooling towers, Mechanical loads, specifications in EN13445, Mechanical vapour compression cycles in refrigeration, Mediatherm, heat transfer medium, Melo, L F, Melting, thermal conduction in, Melting point: Mercury: Merilo correlation, for critical heat flux in horizontal tubes, Merkel's equation, in cooling tower design, Mertz, R, Metais and Eckert diagrams, for regimes of convection: Metals: Metallurgical industry, kilns and furnaces for, Metastable equilibrium, of vapor and liquid, Methane: Methanol: Methyl acetate: Methylacetylene: Methyl acrylate: Methyl amine n-Methylaniline: Methyl benzoate: 2-Methyl-1,3-Butadiene (Isoprene): 2-Methylbutane (isopentane): Methylbutanoate: 2-Methyl-2-butene: Methylcyclohexane: Methylcyclopentane: Methylethylketone: Methyl formate: Metallurgical slag, use of submerged combustion in reprocessing of, Methyl fluorate: 2-Methylhexane: Methylisobutylketone: Methylmercaptan: 1-Methylnaphthalene: 2-Methylnaphthalene: 2-Methylpentane: 3-Methylpentane: 2-Methylpropane (isobutane): 2-Methylpropene: Methyl propionate: Methylpropylether: Methylpropyl ketone: Methyl salicylate: Methyl-t-butyl ether: Microbubbles, for drag reduction, Microchannels (see also microfluidics) Micro-fin tubes: Microfluidics, enhancement of heat transfer in, Mie scattering, in pulverized coal combustion, Miller, C J Miller, E R Mineral oils, as heat transfer media, physical properties of, Mineral wool production, submerged combustion systems for, Minimum fluidization velocity, Minimum heat flux in pool boiling: Minimum tubeside velocity, in shell-and-tube heat exchangers, Minimum velocity for fluidization, Minimum wetting rate, for binary mixtures, Mirror-image concept, in radiative heat transfer,
Radiation Transfer Between Specular and Imperfectly Diffuse Surfaces
Mirrors, spectral characteristics of reflectance from, Mishkinis, D, Mist flow: Mitigation of fouling, Mixed convection occurrence in horiozntal circular pipe, Metais and Eckert diagram for, Mixing (shell-side), in twisted tube heat exchangers, Mixing length, in turbulent flow, Mixtures: Modelling, of fouling: Models, theory of, Modulus of elasticity: Moffat, R S M, Molecular gas radiation properties, Molecular weight: Mollier chart, for humid air, Momentum equation: Monitoring, on line, of fouling, Monochloroacetic acid: Monte Carlo methods, in radiative heat transfer, Moody chart: Morris, M Mostinski correlations: Moving bed, heat transfer to, Muchowski, E, Mueller, A C Muller-Steinhagen, H Multicomponent mixtures: Multidimensional systems, heat conduction in, Multiflux methods, for radiative heat transfer in nonisothermal gases, Multipass shell-and-tube heat exchangers, Multiphase fluid flow and pressure drop: Multiple duties, in plate heat exchangers, Multiple effect evaporation, Multiple hairpin heat exchanger, Multistage flash evaporation (MSF) Multizone model, for furnaces,

Index

HEDH
A B C D E F G H I J K L M
McNaught, J M, Macdonald equation, for fixed-bed pressure drop, Mach number, Macleod-Sugden method for surface tension Macrolayer consumption model for critical heat flux in pool boiling, Maddox, R N Magnetic fields, effect on properties of rheologically complex materials, Magnetic devices, for fouling mitigation, Magnetohydrodynamcs, inaugmentation of heat transfer in microfluidic systems, Margarine manufacture, crystallization of edible oils and fats in, scraped surface heat exchangers for, Marlotherm, heat transfer media, Martensitic stainless steels, Martin, H Martinelli and Boelter equations for combined free and forced convection, Martinelli and Nelson correlations: Mass absorption coefficient, Mass extinction coefficient, Mass fraction, in multicomponent mixtures, Mass scattering coefficient, Mass transfer: Mass transfer coefficient: Materials of construction, for heat exchangers, Low temperature operation, ASME VIII code guidelines for, Matovosian, Robert, Matrix inversion techniques, in radiative heat transfer, Maximum drag reduction Maximum velocities (in shell-and-tube heat exchangers) Maxwell model, for non-Newtonian fluid, Maxwell-Stefan equations, for multicomponent diffusion, Maxwell's equations, for electromagnetic radiation, Mean beam length concept, in radiative heat transfer: Mean phase content, Mean temperature difference: Measurement of fouling resistance, Mechanical design of heat exchangers: Mechanical draft cooling towers, Mechanical loads, specifications in EN13445, Mechanical vapour compression cycles in refrigeration, Mediatherm, heat transfer medium, Melo, L F, Melting, thermal conduction in, Melting point: Mercury: Merilo correlation, for critical heat flux in horizontal tubes, Merkel's equation, in cooling tower design, Mertz, R, Metais and Eckert diagrams, for regimes of convection: Metals: Metallurgical industry, kilns and furnaces for, Metastable equilibrium, of vapor and liquid, Methane: Methanol: Methyl acetate: Methylacetylene: Methyl acrylate: Methyl amine n-Methylaniline: Methyl benzoate: 2-Methyl-1,3-Butadiene (Isoprene): 2-Methylbutane (isopentane): Methylbutanoate: 2-Methyl-2-butene: Methylcyclohexane: Methylcyclopentane: Methylethylketone: Methyl formate: Metallurgical slag, use of submerged combustion in reprocessing of, Methyl fluorate: 2-Methylhexane: Methylisobutylketone: Methylmercaptan: 1-Methylnaphthalene: 2-Methylnaphthalene: 2-Methylpentane: 3-Methylpentane: 2-Methylpropane (isobutane): 2-Methylpropene: Methyl propionate: Methylpropylether: Methylpropyl ketone: Methyl salicylate: Methyl-t-butyl ether: Microbubbles, for drag reduction, Microchannels (see also microfluidics) Micro-fin tubes: Microfluidics, enhancement of heat transfer in, Mie scattering, in pulverized coal combustion, Miller, C J Miller, E R Mineral oils, as heat transfer media, physical properties of, Mineral wool production, submerged combustion systems for, Minimum fluidization velocity, Minimum heat flux in pool boiling: Minimum tubeside velocity, in shell-and-tube heat exchangers, Minimum velocity for fluidization, Minimum wetting rate, for binary mixtures, Mirror-image concept, in radiative heat transfer,
Radiation Transfer Between Specular and Imperfectly Diffuse Surfaces
Mirrors, spectral characteristics of reflectance from, Mishkinis, D, Mist flow: Mitigation of fouling, Mixed convection occurrence in horiozntal circular pipe, Metais and Eckert diagram for, Mixing (shell-side), in twisted tube heat exchangers, Mixing length, in turbulent flow, Mixtures: Modelling, of fouling: Models, theory of, Modulus of elasticity: Moffat, R S M, Molecular gas radiation properties, Molecular weight: Mollier chart, for humid air, Momentum equation: Monitoring, on line, of fouling, Monochloroacetic acid: Monte Carlo methods, in radiative heat transfer, Moody chart: Morris, M Mostinski correlations: Moving bed, heat transfer to, Muchowski, E, Mueller, A C Muller-Steinhagen, H Multicomponent mixtures: Multidimensional systems, heat conduction in, Multiflux methods, for radiative heat transfer in nonisothermal gases, Multipass shell-and-tube heat exchangers, Multiphase fluid flow and pressure drop: Multiple duties, in plate heat exchangers, Multiple effect evaporation, Multiple hairpin heat exchanger, Multistage flash evaporation (MSF) Multizone model, for furnaces,
N O P Q R S T U V W X Y Z
M Mirror-image concept, in radiative heat transfer,
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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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