A limiting approach for the evaluation of geometric mean transmittance in a multidimensional absorbing and isotropically scattering medium
Abstract
The calculation of the geometricmean transmittance factor between areas with an intervening absorbing and isotropically scattering medium is considered. While an exact expression for the factor is shown to be quite complicated, the upper and lower limits of the factor can be readily generated from physical considerations. Integral expressions for successively increasing (decreasing) values of the lower (upper) limits are obtained. For twodimensional systems, these expressions are reduced to integrals involving S sub n(x), a class of exponential integral function that has been tabulated in a previous work. Utilizing the kernel substitution technique, these integrals are evaluated analytically in closed form for some selected geometries. For cases with small optical thickness and large scattering albedo, both limits are shown to converge relatively slowly to the actual transmittance factor. But the decreasing difference between the two limits provides accurate estimate of the geometricmean transmittance factor. Based on these results, some interesting conclusions concerning the effect of scattering on multidimensional radiative transmission are established.
 Publication:

ASME Journal of Heat Transfer
 Pub Date:
 May 1984
 Bibcode:
 1984ATJHT.106..441Y
 Keywords:

 Absorbers (Materials);
 Isotropic Media;
 Radiative Heat Transfer;
 Scattering;
 Transmittance;
 Albedo;
 Approximation;
 Convergence;
 Integral Equations;
 Optical Thickness;
 Photoabsorption;
 Fluid Mechanics and Heat Transfer