Numerical study of convective heat transfer and fluid flow through porous media

Abstract

Lattice Boltzmann method (LBM) is applied to predict the phenomenon of natural convection in a generalised isotropic porous media model filled in a square geometry by introducing a force term to the evolution equation and porosity to the density equilibrium distribution function. The temperature field is obtained by simulating a simplified thermal model which uses less velocity directions for the equilibrium distribution function and neglects the compression work done by the pressure and the viscous heat dissipation. The reliability of this model for natural convective heat transfer simulation is studied by comparing with results from other previous simulations at a porosity value, e = 0.9999 which is close to unity resembling a square cavity condition. The model is then used for simulation at e equal to 0.4, 0.6 and 0.9. The results obtained are discussed in terms of the Nusselt number, streamlines and isotherms. Comparison with previous works confirms the applicability of the model.