The subject dealt with is an accurate semi-analytical modeling of two-dimensional radiative heat transfer. The semi-transparent medium is gray and has an absorbing-emitting rectangular shape hollowed by internal square fluid cavity, bounded by black surfaces. The aim is to establish some benchmark results either for radiative intensity, or flux and temperature field, from which forwards analysis will be compared. Hence, analytical incoming radiative intensity, flux and temperature fields inside the gray medium are established, in function of the center coordinates of the fluid cavity. Only radiative transfer mode is considered at equilibrium state. Therefore, radiative quantities are spatially and angularly integrated using special functions in order to avoid ray effects on results. Thanks to double Gauss quadrature, which will allow to obtain numerically the radiative equations. Finally, results validation is done when the size of internal hollowed cavity becomes very small and expected results remain with good agreement with literature.
The present paper deals with an exact semi-analytical formulation of a combined conductiveradiative 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.
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