Combined conduction and radiation heat transfer in a gray anisotropically scattering planar medium with diffuse-specular boundaries

Abstract

Coupled conduction and radiation heat transfer in a gray planar nonlinearly anisotropic scattering medium bounded between two plane parallel surfaces reflecting both diffusely and specularly is analyzed. The governing integrodifferential equations are solved by a numerical iterative method consisting of Numerov's method to solve the energy equation and Chandarsekhar's discrete ordinates method in conjunction with the Crank-Nicolson method to solve the radiative transfer equation. Convergence of the solution is enhanced by Ng-acceleration. The numerical algorithm described is found to be fast and reliable. Numerical results based on S₃₂ method indicate that anisotropy plays an important role, and difference between the diffuse and specular reflections is found to be insignificant.