Modeling of the radiative contribution to heat transfer in porous media composed of spheres or cylinders

A theoretical model for evaluating the radiative conductivity tensor of a porous media is developed in this paper. The porous media is composed of a transparent fluid and opaque particles with characteristic lengths longer than the radiation wavelength. The main features of the proposed approach are (i) take into account the interaction between conduction and radiation heat transfers, (ii) allow the modeling of the radiative transfer in anisotropy system such as an assembly of cylinders, and (iii) have an easy numerical implementation into the energy equations of the porous media. In order to study the accuracy of the approach, the paper evaluates the model for porous media composed of spheres or cylinders. The predictions of the model agree well with experimental data and with results obtained from finite element simulations. The numerical results also show that the radiative conductivity can be strongly influence by the effect of temperature distribution across the particle surface and by the effect of the multiple scattering of radiation in the porous media.