Conductive-radiative heat transfer in a 2D semi-transparent medium with a square centered obstacle

Abstract

The present paper deals with an exact semi-analytical formulation of a combined conductive-radiative heat transfer, applied to a two-dimensional semi-transparent medium carrying a square centered obstacle. The gray participating medium with black boundaries absorbs, emits but does not scatter radiation. One intends to evaluate the temperature and radiative heat flux distributions within the semi-transparent medium. The radiative transfer equation has been solved using an exact analytical expansion of Bickley-Naylor and Altaç angular integrated Bickley-Naylor functions, then solved numerically with Gauss quadrature. Energy equation has been directly discretized and approximated numerically using the centered finite differences method and consequently the dimensionless temperature has been obtained after an iterative scheme. The results of radiative quantities obtained have been verified with benchmark with an excellent agreement, both for simple and complex geometries. Simulations have been performed to obtain results for different sizes of the centered obstacle and the optical thickness. The effects of the conduction-radiation parameters, discrete directions and the size of the obstacle have also been investigated.