POLYNOMIAL APPROXIMATION SOLUTION OF HEAT TRANSFER BY CONDUCTION AND RADIATION IN A ONE-DIMENSIONAL ABSORBING, EMITTING, AND SCATTERING MEDIUM

Abstract

A polynomial approximation method for the solution of heat transfer by conduction and radiation in an absorbing, emitting, and isotropically scattering medium has been developed. Consideration is given to a one-dimensional system bounded by two parallel gray, diffuse, isothermal walls. A function f(t) representing the relation between incident radiation and temperature is defined and approximated by a polynomial equation over the entire optical thickness. The integrodifferential equation is transformed, by introducing radiation operators, into simple expressions, which are then solved iteratively. The method of solution is shown to be relatively simple and converges very quickly to the exact solutions.