Numerical analysis of conjugate natural convection and thermal surface radiation in a cube filled with diathermanous medium

Mathematical simulation of convective-conductive-radiative heat transfer in a cubical cavity filled with diathermanous medium has been carried out. The domain of interest is a closed volume having heat-conducting solid walls of finite thickness with diffuse grey inner surfaces. The outer surfaces of two vertical walls are isothermal while the other walls are adiabatic. The boundary-value problem has been formulated in dimensionless variables such as “vector potential–vorticity vector–temperature” in the Boussinesq approximation and taking into account the diathermancy of the continuous medium. An analysis of surface thermal radiation has been conducted on the basis of the net-radiation method in the form of Poljak. The formulated transient boundary-value problem has been solved by finite difference method in a wide range of the Rayleigh number, thermal conductivity ratio and surface emissivity. Correlations for the average convective and radiative Nusselt numbers at the characteristic internal solid-fluid interface have been obtained. The comparison between the obtained three-dimensional results and the two-dimensional data has been conducted. It has been found, that on the basis of a three-dimensional model it is possible to analyze the formation of intensive transverse flows from two vertical surfaces which are absent in a two-dimensional model. It has been also shown, that the solution of convective-radiative heat transfer problems in the conjugate statement leads to essential changes in distributions of local and integral parameters in comparison with the non-conjugate model, which first of all is related to a more correct description of the thermal radiation in diathermanous media due to taking into account the thermal conduction of the solid walls.