A lattice Boltzmann model for thermal non-Newtonian fluid flows through porous media

Abstract

Following recent studies by Huilgol and Kefayati [1,2], that developed a thermal Lattice Boltzmann method for different non-Newtonian fluids, we propose, in this paper, a general lattice Boltzmann method for thermal incompressible non-Newtonian fluids through porous media. Since no restrictions are placed on the constitutive equations in this method, the theoretical development can be applied to all fluids, whether they be Newtonian, or power law fluids, or viscoelastic and Bingham fluids. To validate the accuracy of the method, natural convection in a porous cavity was studied and compared with previous studies. Next, we employ the model to simulate natural convection of power-law and Bingham fluids in a porous cavity.