Radiation Transfer in Isotropically Scattering, Rectangular Enclosures

Abstract

Radiative heat transfer in absorbing, emitting, isotropically scattering, gray, two-dimensional rectangular regions having an emitting boundary and spacially distributed energy sources is solved by both the collocation and the Galerkin methods. Using the expressions given in this work, the quantities, such as the incident radia- tion, the radiation heat flux, and the divergence of the radiation heat flux anywhere in the medium, can be deter- mined to a high degree of accuracy for all values of the single scattering albedo, from small to moderately large values of horizontal and vertical optical dimensions of the enclosure. Results are presented for representative cases, to illustrate the application of the method. A parameter study is made to show the effects of the single scattering albedo on the incident radiation and the heat flux. HERE are numerous situations in which radiation heat transfer in absorbing, emitting, isotropically scattering, gray, two-dimensional rectangular media is important. They include, among others, modeling of heat transfer in fur- naces, fire protection, manufacturing of glass, studies of in- sulation properties of various types of fibrous and foam materials, cryogenics, and heat transfer through partially transparent materials. In order to study radiation heat transfer in any one of these situations, it is necessary to solve the equation of radiative heat transfer. Numerous approximate and exact methods of analysis have been reported for solving the equa- tion of radiative transfer in a one-dimensional medium; but for the two-dimensional situation, the problem of an absorb- ing and emitting medium has been studied with approximate methods of analysis by several investigators including Modest,1 Razzaque et al., 2 and Fiveland.3 In the case of a scattering medium, the source function expansion technique has been used by Sutton and Ozisik4; a numerical integration scheme has been employed by Crosbie and Schrenker5 to study the problem of diffuse incident radiation and no energy sources in the medium; and the same numerical technique has been applied by Crosbie and Schrenker6 to solve the problem of collimated incident radiation and no energy sources in the medium. Further information, with regard to solution methods and areas of applications of radiative heat transfer, is given in a recent survey by Viskanta.7 We present a highly accurate method for solving two- dimensional radiation transfer in an absorbing, emitting, isotropically scattering, two-dimensional rectangular en- closure. In the following sections, the method of analysis is described first. Results are then presented that can be used to check the accuracy of various approximate methods of analysis. Finally, a parameter survey is made to examine the effects of single scattering albedo on the radiation heat transfer for various optical dimensions of the medium.