Effect of thermal radiation on temperature differential in a porous medium under local thermal non-equilibrium condition

The present work examines numerically the effect of thermal radiation from the solid phase on the fluid and solid temperature fields inside a porous medium by studying forced convection heat transfer process within a pipe filled with a porous material. The Darcy-Brinkman-Forchheimer model is utilized to represent the fluid transport within the porous medium. A local thermal non-equilibrium (LTNE), two-equation model is used to represent the energy transport for the solid and fluid phases. The radiative transfer equation is solved by discrete ordinate method (DOM) to compute the radiative heat flux in the porous medium. Two primary approaches (models A and B) are used to represent the boundary conditions for constant wall heat flux. Firstly for a fixed model, the effects of radiative heat transfer from the solid phase on the temperature profiles of the two phases are analyzed for different parameters such as porosity, Darcy number, solid-to-fluid thermal conductivity ratio and inertia parameter. Secondly, the effects of radiative heat transfer on the temperature distributions and Nusselt numbers for the two phases are examined by comparing the result obtained by application of models A and B. The results demonstrate that ignoring the effect of thermal radiation from the solid phase leads to a substantial error in prediction of the solid and fluid temperature fields and validity of the local thermal equilibrium (LTE) between the two phases. The solid and fluid temperature fields obtained for the radiative case are substantially lower than those obtained for the non-radiative case. Further, it is seen that the thermal radiation from the solid phase leads the temperature fields to the LTE condition. Depending on the pertinent parameters and compared to the non-radiative case, for the radiative case up to 50% decrease in the non-dimensional temperature differential is computed between the two phases. The Nusselt number obtained by application of model A for the radiative case is higher than those predicted for the non-radiative case. While, for model B the fluid Nusselt numbers obtained for the radiative and non-radiative cases are similar.