Analysis of two-dimensional radiative heat transfer in a gray medium with internal heat generation

Abstract

Radiative heat transfer in a two-dimensional rectangular enclosure with gray medium and internal heat generation is considered. Solutions are generated by a point allocation technique in which unknown temperature profiles are expressed as polynomials. Based on a recently developed generalized exponential integral function, the present solution technique is demonstrated to be computationally more efficient than most of the conventional solution methods. For the case with constant internal heat generation, numerical solutions for temperature and heat flux distributions for enclosures of different optical thicknesses and aspect ratios are obtained. Analytical solutions are developed in the optically thin limit. Both the optical thickness and the enclosure geometry are demonstrated to have strong effects on the temperature distribution within the medium. The average heat transfer to the different boundaries, on the other hand, appears to depend mainly on the enclosure geometry.