The Influence and Treatment of Mie-Anisotropic Scattering in Radiative Heat Transfer

1980 ◽  
Vol 102 (1) ◽  
pp. 92-98 ◽  
Author(s):  
M. F. Modest ◽  
F. H. Azad
Keyword(s):  
Heat Transfer ◽  
Radiative Heat Transfer ◽  
Legendre Polynomial ◽  
Phase Function ◽  
Radiative Heat ◽  
Anisotropic Scattering ◽  
Mie Scattering ◽  
Differential Approximation ◽  
Temperature Distributions ◽  
Polynomial Series

The influence of highly anisotropic Mie scattering on radiative heat transfer is investigated. Exact solutions for temperature distributions and radiative flux are found for scattering functions with up to 35 terms in their Legendre polynomial series expansion. Approximation by linear anisotropic scattering is found to describe radiative transfer excellently as long as the phase function is relatively smooth and as long as there is only insignificant backscattering. The linear-anisotropic differential approximation also yields very accurate results (within its limitations) and can account for backscattering as well.

Radiative Heat Transfer in Multidimensional Emitting, Absorbing, and Anisotropic Scattering Media—Mathematical Formulation and Numerical Method

1989 ◽  
Vol 111 (1) ◽  
pp. 141-147 ◽  
Author(s):  
Zhiqiang Tan
Keyword(s):  
Heat Transfer ◽  
Integral Equations ◽  
Radiative Heat Transfer ◽  
Radiative Heat ◽  
Numerical Technique ◽  
Mathematical Formulation ◽  
Internal Heat ◽  
Anisotropic Scattering ◽  
Scattering Media ◽  
Zonal Method

Thermal radiative transmission in multidimensional emitting, absorbing, and anisotropic scattering media is studied in this paper. In the first part, starting from basic formulae of radiative heat transfer, a set of integral equations for the problem is derived. Then the product-integration method is applied to discretize the integral equations. This method, while analogous to Hottel’s zonal method or Razzaque’s finite element method, requires evaluation of only three or two-dimensional integrals for three-dimensional systems. Finally the formulation and the numerical technique are applied to the problems of thermal radiation in emitting, absorbing, and linearly anisotropic scattering planar and square media with gray surfaces and with or without internal heat generations. Computed results are discussed and compared with available data.

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