A NUMERICAL STUDY OF SOME RADIATIVE HEAT TRANSFER PROBLEMS IN PARTICIPATING MEDIUM

Abstract

The aim of this study is to investigate radiative heat transfer in a participating medium which absorbs, emits and scatters radiation. In chapter l, we give an introdnction to the basic terminology used in this work and the equation of radiative heat transfcr is derived. In chapter 2, we consider radiative heat transfer in a two-dimensional rectangular participating medium exposed to emitting and reflecting boundaries on the top and on the bottom. A finite difference scheme is applied to discretize the transfer equation and a product quadrature scheme is devised to compute the source function. Results of the incident intensity are compared with that of Wu (1990) and Thynell et al (1978). In chapter 3, we consider radiative heat transfer in a two-dimensional annular rectangle participating medium (i.e. a rectangular medium in which a smaller rectangle in the centre is being removed.) The medium is exposed to emitting and reflecting boundaries at the inner and outer surfaces. The same finite difference scheme as in chapter 2 is applied to discretize the transfer equation. The product quadrature in chapter 2 is modified to compute the source function. Results of the incident intensity are presented for different parameters. In chapter 4, we look at the thermal ignition of radiatively active particles suspended in a slab bounded by two parallel walls. The medium consists of air and carbon particles. The air is assumed to be transparent to radiation. The carbon particles are assumed to be radiatively active. It absorbs, emits and scatters radiation. We introduce a quadrature collocation method to solve the coupled integro-differential equations of transfer. The ignition delay of carbon particles is being studied for isotropic scattering. Our results of the ignition delay of carbon particles for non-scattering case agree well with that of Back (1990). The results for the more difficult scattering case with singular integrals is the main contribution of this chapter.