Lattice Boltzmann numerical simulation and entropy generation analysis of natural convection of nanofluid in a porous cavity with different linear temperature distributions on side walls

In this paper, natural convection in a porous cavity filled with Cu-water nanofluid is investigated using Lattice Boltzmann method (LBM). Horizontal walls of the cavity are adiabatic and vertical walls have a fixed linear temperature distribution. The effect of different boundary conditions on heat transfer characteristics is investigated and results are compared with each other. Fluid flow through porous media has been modelled by Ergun's relation and an in-house parallel LBM computational code is developed by using Bhatnagar-Gross-Krook model with additional force terms to account the porous medium and gravity effects. Effects of different boundary conditions (four cases) on heat transfer characteristics are investigated at different Rayleigh, Darcy and nanoparticle concentrations, and results are illustrated in terms of stream function, temperature distribution, Nusselt, relative Nusselt, flow circulation speed and entropy generation. For high and low Ra values, case D (the hottest and coldest points are at the top of cavity) and case C (the hottest and coldest points are placed at the top and bottom of the hot and cold walls respectively) show the best heat transfer performance, respectively. Also a decrement in Da, decreases Nu and an optimal Ra exists to maximize the relative Nu for each Da.