Numerical simulation of natural convection in a porous cavity with internal hot and cold sources using the lattice Boltzmann method

Abstract

Based on the non-orthogonal multiple-relaxation-time lattice Boltzmann method (MRT–LBM), natural convection in a porous square cavity with a pair of isothermally hot and cold blocks inside was studied numerically in the current study. The influence of arrangements (Cases 1, 2, 3, 4, and 5), spacing ratio (S), and size ratio (A) of the hot and cold sources and the Rayleigh number (Ra) on the heat exchange efficiency were studied. The results show that different arrangements produce different heat-transfer effects. Two arrangements, hot and cold blocks placed horizontally (Case 1) and a cold block located in the upper left corner while a hot block is located in the bottom right corner (Case 4), have better heat exchange performance than the other three cases because the flow directions of hot and cold fluids are closer to that of the heat transfer. Then, the influence of the spacing between blocks and the size of the blocks on the heat transfer rate was further studied in Cases 1 and 4. Heat transfer performance improved with increasing A. Additionally, the variation in the heat transfer performance with spacing is related to the arrangement and size ratio of the blocks. For Ra = 104, 105, and 106, the best heat transfer characteristics were obtained in Case 1 when S = 0.05 and A = 0.20. For Ra = 107, Case 4 exhibited the best heat transfer effect when S = 0.35 and A = 0.20.