An efficient computational technique for radiative heat transfer in axisymmetric enclosures

Abstract

One of the most important mechanisms of heat transfer in furnaces and other similar equipment is radiation. Radiative heat transfer can be rigorously described by the radiative transfer equation, which is a six-dimensional integro-differential equation in a phase space. The most popular and widely adopted techniques for solving the radiative transfer equation are the P1 approximation and the S4 method. Although the P1 approximation solves the radiative transfer equation with a decent amount of computer time, it yields somewhat inaccurate results for the cases of optically thin media. On the contrary, the S4 method yields accurate results for all ranges of optical thickness but it requires a large amount of computer time and memory. Moreover, the number of iterations in the S4 method, and consequently the computer time, increases as the value of the scattering albedo increases when the extinction coefficient is not small. In the present work, a new algorithm is devised to solve the radiative heat transfer equation efficiently. This algorithm consists of separating the radiation intensity into two parts i.e., wall emission and medium emission according to the modified differential approximation. Then the wall emission is treated by the S4 method, which can satisfy the wall boundary conditions exactly, and the medium emission is treated by the P1 approximation. The scattering term which increases the iteration number in the S4 method is taken care of by the P1 approximation. The present algorithm solves the radiative heat transfer equation accurately and efficiently for all ranges of optical thickness when compared with conventional techniques, and may be adopted in the analysis of many engineering systems with a significant amount of radiative heat transfer such as pulverised coal-fired furnaces.