Exact Solutions for Radiative Heat Transfer in Box-Shaped Furnaces

Abstract

Exact expressions for the distributions of the components of radiative flux density and the radiative energy source term in terms of wall and medium temperature distributions have been formulated for an emitting-absorbing medium of constant properties bounded by black walls of a box-shaped enclosure. The accuracy of numerical solutions has been tested on an idealized enclosure for which exact analytical solution of the expressions is possible and shown to have good accuracy. The exact expressions have then been solved numerically for an enclosure problem based on data reported previously on a large-scale experimental furnace. The principal feature of the data is highly nonuniform medium and wall temperature distributions which are typical of the conditions encountered in industrial furnaces. These data have been chosen because of their practical importance and the nonavailability of exact solutions for such data. The resulting exact solutions have been given in tabular form and are intended to serve in the future as standards for testing the accuracy of the approximate predictions produced using various three-dimensional flux models.