Analysis of the conduction–radiation problem in absorbing, emitting, non-gray planar media using an exact method

Abstract

Systems in which both conduction and radiation are the dominant modes of heat transfer are important in many engineering applications and various numerical methods exist to analyze such systems. An exact solution to the conduction–radiation problem in a one-dimensional, planar, absorbing, emitting, non-gray medium is presented. The method uses an integrating factor to solve the radiative transfer equation and variation of parameters is used to solve the energy equation. The model is verified by comparing the temperature profiles calculated from this work to those found using numerical methods for both gray and non-gray cases.