Natural Convection of Power Law Fluid through a Porous Deposit: MRT-LBM Approach

Abstract

In this research, natural convection of power law fluid in a square cavity, with a porous deposit in the shape of a semi-cylinder is studied numerically, using the multiple-relaxation-time lattice Boltzmann method. The modified Darcy-Brinkman model is applied for modelling the momentum equations in porous medium and the Boussinesq assumption is adopted to model the buoyancy force term. The influences of power law index (0.6 ≤ n ≤ 1.4), Darcy number (10−5 ≤ Da ≤ 10−2), Rayleigh number (103 ≤ Ra ≤ 106) and the radius ratio of the semi-cylindrical porous deposit (0.05 ≤ R ≤ 0.5) on hydrodynamic and heat transfer are studied. The obtained results show that these parameters have an important effect, on the structure of hydrodynamic and thermal transfer. The improvement of the power law index leads to a decrease in the heat transfer rate, illustrated by the average Nusselt number, and the augmentation in Darcy number induces an increase in that rate. Moreover, the variation of the Rayleigh number and the porous deposit radius has a significant effect on the transfer rate and convective structure. Besides, an unusual phenomenon is noticed for high Rayleigh numbers, where a better heat evacuation from the porous deposit is noticed for the dilatant fluid compared to the pseudoplastic one.

Keywords

• modified darcy-brinkman model; square cavity; semi-cylinder.