DOUBLE SPHERICAL-HARMONICS APPROXIMATION APPLIED TO COMBINED CONDUCTION-RADIATION IN A PLANAR MEDIUM

Abstract

Steady, combined radiation and conduction heat transfer in an absorbing, emitting and anisotropically-scattering planar material is investigated theoretically. The medium boundaries are assumed with specified temperatures. Emitting and diffusely reflecting boundaries are considered. The influence of radiation heat transfer is obtained by solving the differential-integral equation with the double spherical harmonics (DP1) approximation technique. This technique reduces the integral-differential equation of radiative transfer into systems of first-order differential equations. The resulting set of coupled first order ordinary differential equations is solved as a boundary value problem utilizing software routines that are readily available. The integral energy equation is solved by the Simpson's method with an iterative procedure. In order to demonstrate the versatility and accuracy of the proposed methodology, the results of several numerical experiments are presented and compared with benchmark solutions. The method of solution is shown to be relatively simple and in close agreement with exact solutions.