A high order approximation, the method—a mnemonic for synthetic kernel—is proposed for solving radiative transfer problems in participating medium. The method relies on approximating the integral transfer kernel by a sum of exponential kernels. The radiative integral equation is then reducible to a set of coupled second-order differential equations. The method is tested for one-dimensional plane-parallel participating medium. Three quadrature sets are proposed for the method, and the convergence of the method with the proposed sets is explored. The solutions are compared with the exact, and solutions. The and approximations using quadrature Set-2 possess the capability of solving radiative transfer problems in optically thin systems.
The Approximation for Solving Radiative Transfer Problems in Absorbing, Emitting, and Isotropically Scattering Plane-Parallel Medium: Part 1
Contributed by the Heat Transfer Division for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received by the Heat Transfer Division March 15, 2000; revision received October 9, 2001. Associate Editor: C. T. Avedisian.
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Altac¸, Z. (July 16, 2002). "The Approximation for Solving Radiative Transfer Problems in Absorbing, Emitting, and Isotropically Scattering Plane-Parallel Medium: Part 1 ." ASME. J. Heat Transfer. August 2002; 124(4): 674–684. https://doi.org/10.1115/1.1464130
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