Effects of pore geometry on the natural convective heat transmission in a porous cavity: a lattice Boltzmann simulation

In this study, a two-dimensional investigation on natural convection inside a porous cavity at pore-scale is performed using the lattice Boltzmann method with the focus on the effects of pores geometry. The model is independent of the shape, density, porosity, and arrangements of the pores, because the image of the porous cavity is binarized and given to the code as input. The influences of pores geometry, Rayleigh number, porosity, and pore/liquid thermal diffusivity ratio are studied. A D2Q9 multi-relaxation time and a D2Q9 single-relaxation time lattice Boltzmann model are used for the flow and energy equations, respectively, with two separate distribution functions approach. For this purpose, pores with square, circular, and star shapes are considered. The Rayleigh number is varied in the range of 10(3) to 10(6) for three different porosity values (0.43, 0.71, 0.85) and pore/liquid thermal diffusivity ratios of 6, 70, and 788, with water and air as working fluids. Local variations of hot wall Nusselt number revealed that the star, circular, and square pores have the highest peak values of the local Nusselt number, respectively. By contrast, the lowest local values occur in the porous cavity with circular pores. In the examined porous media, the maximum increase in the hot wall averaged Nusselt number is equal to 24.3% occurring at epsilon=0.71, when pores are varied from circular to star shapes at Ra = 10(4). Moreover, using the star pores with a porosity value of 0.43, the averaged Nusselt number on the hot wall is increased by 184.46% compared to the empty cavity at Ra = 10(3). Besides, it is shown that increasing the thermal diffusivity ratio higher than 70 has little effect on the hot wall averaged Nusselt number.