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Received: 25 Jauary 2019 Accepted: 20 April 2019 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.

Modeling of Radiative Heat Transfer in a Gray Semi-transparent Medium with Internal Fluid Cavity Limited by Black Boundary Surfaces