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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,
Gas Radiation Properties
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, 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,
Gas Radiation Properties
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, 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 Mass scattering coefficient,
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Gas Radiation Properties

DOI 10.1615/hedhme.a.000208

2.9 HEAT TRANSFER BY RADIATION
2.9.5 Gas radiation properties

D.K. Edwards

A. The equation of transfer

Up to this point, a diathermanous medium has been assumed. In such a medium the radiant intensity I of a stream of photons is unaffected by passage through the medium. More generally, the photons and matter interact. Three processes may be distinguished: (1) net absorption (total absorption minus induced emission), (2) spontaneous emission, and (3) scattering. The latter can be broken down into scattering out of the beam and scattering into the beam. The result is that in slant path increment ds there is an incremental change in intensity dI as pictured in Figure 1. The equation giving dI/ds is named the equation of transfer.

Figure 1 Change of intensity I along incremental path length ds

The absorption, emission, and scattering properties of matter are sometimes characterized by cross sections. For example, visualize a spherical oil droplet such as is sprayed into a combustion chamber. The droplet of radius R has a total surface area of 4πR2, but its projected area is πR2. The latter is said to be the geometric cross section. If one examines the shadow behind a droplet that is large compared to the wavelength, one finds, due to diffraction, a shadow area of 2πR2 but a bright halo contains half of the radiant power missing due to the shadow, half of I dΩ 2πR2. Whether the droplet is large or small, the radiant power missing from the incident beam divided by that incident on an area of πR2 is termed the extinction efficiency Qe. Thus if one considers the halo radiation as scattered, that is, caused to deviate in direction, the extinction efficiency of a large particle is 2; but, if one considers the halo as undeviated, a more reasonable view for engineering power transfer calculations, then Qe is 1 for a large particle.

The power missing from the shadow may have been absorbed, or it may have been scattered into other directions. The fraction scattered into other directions is called the albedo for single scatter ωs. The fraction 1 – ωs is sometimes called the particle emissivity. Actually it would be better called the particle absorptivity, but Kirchhoff’s law is invoked. The quantity ωsQe is called the scattering efficiency Qs, and (1 – ωs)Qe is called the absorption efficiency Qa.

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