A unified numerical model for simulating heat transfer in flows past porous bodies

A unified numerical model for simulating thermal flows past and through porous media whose thermal properties are identical with those of the surrounding fluid is proposed in this paper, which advances the work of the unified immersed boundary-lattice Boltzmann flux solver (UIB-LBFS). The proposed method greatly simplifies the conventional computation procedure for thermal flows past porous bodies by unifying the governing equations for the flow and temperature fields in both the porous and fluid domains. This is achieved by introducing a diffuse layer, across which the variation of the flow properties including its thermal features are expected to be smooth. Also, the developed method can be applied on either uniform or nonuniform grid since the numerical fluxes are locally reconstructed by LBFS at cell interfaces. In addition, the boundary conditions for both the flow and temperature fields at the porous-fluid interface with complex shape can be implemented through IBM in a simple way. The proposed method is validated by several numerical examples over wide ranges of thermal parameters from forced convection to mixed convection. Excellent agreements are obtained for all simulations, including the one with severe temperature gradient in the thin temperature boundary layer at Pr = 10, which demonstrates the capabilities of the proposed method.