Exact solution of the equation of radiative transfer for semi-infinite plane-parallel isotropic scattering atmosphere with scattering albedo ?0 ? 1 by a method based on Laplace transform and Wiener-Hopf technique

1978 ◽  
Vol 57 (2) ◽  
pp. 419-427 ◽  
Author(s):  
Rabindra Nath Das
Keyword(s):  
Exact Solution ◽  
Radiative Transfer ◽  
Laplace Transform ◽  
Isotropic Scattering ◽  
Infinite Plane ◽  
Plane Parallel

The SKN Approximation for Solving Radiative Transfer Problems in Absorbing, Emitting, and Linearly Anisotropically Scattering Plane-Parallel Medium: Part 2

2002 ◽  
Vol 124 (4) ◽  
pp. 685-695 ◽  
Author(s):  
Zekeriya Altac¸
Keyword(s):  
Radiative Transfer ◽  
Incident Energy ◽  
Radiative Heat ◽  
Isotropic Scattering ◽  
Benchmark Problems ◽  
Scattering Medium ◽  
Second Order Differential Equations ◽  
Plane Parallel ◽  
Kernel Approximation ◽  
Transfer Problems

The SKN (Synthetic Kernel) approximation is proposed for solving radiative transfer problems in linearly anisotropically scattering homogeneous and inhomogeneous participating plane-parallel medium. The radiative integral equations for the incident energy and the radiative heat flux using synthetic kernels are reduced to a set of coupled second-order differential equations for which proper boundary conditions are established. Performance of the three quadrature sets proposed for isotropic scattering medium are further tested for linearly anisotropically scattering medium. The method and its convergence with respect to the proposed quadrature sets are explored by comparing the results of benchmark problems using the exact, P11, and S128 solutions. The SKN method yields excellent results even for low orders using appropriate quadrature set.

scholarly journals Exact and unique solution of a transport equation in a semi-infinite medium by Laplace transform and Wiener-Hopf technique

2004 ◽  
Vol 35 (4) ◽  
pp. 347-350
Author(s):  
Z. Islam ◽  
A. Mukherjee ◽  
S. Karanjai
Keyword(s):  
Radiative Transfer ◽  
Laplace Transform ◽  
Transport Equation ◽  
Unique Solution ◽  
Optical Depth ◽  
Axial Symmetry ◽  
Diffuse Reflection ◽  
Infinite Medium ◽  
Plane Parallel ◽  
Emergent Intensity

The equation of radiative transfer in non-conservative case for diffuse reflection in a plane-parallel semi-infinite atmosphere with axial symmetry has been solved by Laplace transform and Wiener-Hopf technique. We have determined the emergent intensity in terms of Chandrasekhar's H-function and the intensity at any optical depth by inversion.

The transport equation of radiative transfer with isotropic scattering

1969 ◽  
Vol 65 (1) ◽  
pp. 199-208 ◽  
Author(s):  
G. E. Hunt
Keyword(s):  
Integral Equation ◽  
Radiative Transfer ◽  
Singular Integral Equation ◽  
Transport Equation ◽  
Singular Integral ◽  
Source Function ◽  
Three Dimensional ◽  
Isotropic Scattering ◽  
Plane Parallel ◽  
Homogeneous Plane

AbstractThe kernel of the integral equation for the source function in a three-dimensional homogeneous atmosphere possesses the properties of a Green's function. These properties are used to transform the integral equation into a singular integral equation for the kernel. The particular case of a homogeneous plane parallel atmosphere is discussed and a solution to the kernel equation is obtained at all points of the atmosphere.

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