scholarly journals Closure to “Discussions of ‘Radiative Heat Transfer Between Parallel Plates Separated by a Nonisothermal Medium With Anisotropic Scattering’” (1967, ASME J. Heat Transfer, 89, p. 204)

1967 ◽  
Vol 89 (3) ◽  
pp. 204-204
Author(s):  
H. M. Hsia ◽  
T. J. Love
Keyword(s):  
Heat Transfer ◽  
Radiative Heat Transfer ◽  
Radiative Heat ◽  
Anisotropic Scattering ◽  
Parallel Plates

Radiative Heat Transfer Between Parallel Plates Separated by a Nonisothermal Medium With Anisotropic Scattering

1967 ◽  
Vol 89 (3) ◽  
pp. 197-203 ◽  
Author(s):  
H. M. Hsia ◽  
T. J. Love
Keyword(s):  
Heat Transfer ◽  
Radiative Heat Transfer ◽  
Radiative Heat ◽  
Radiant Energy ◽  
Anisotropic Scattering ◽  
Temperature Profiles ◽  
Parallel Plates ◽  
Integral Term ◽  
Isothermal Temperature ◽  
Radiative Transport Equation

The problem of radiative heat transfer in a nonisothermal medium is considered. The analysis is carried out for a plane parallel atmosphere separated by a cloud of particles which scatters radiant energy in an anisotropic fashion. Linear and isothermal temperature profiles are compared for enclosures with partially reflecting diffuse boundaries. The solutions are obtained by representing the integral term of the radiative transport equation by a quadrature. The resulting set of nonhomogeneous differential equations are solved utilizing the method of idempotents.

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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