Lattice Boltzmann Modeling for Natural Convection in a Square Cavity Partially Heated and Filled with a Non-Newtonian Fluid: Analysis of Combined Effects of a Magnetic Field and Internal Heat Generation

The combined impact of a Lorentz force and volumetric heat generation on natural convection heat transfer and fluid flow in a square cavity are investigated numerically using MRT-LBM. The cavity is filled with a non-Newtonian fluid and submitted to a partial heating from below. The main physical parameters controlling the problem are the Hartmann number ( \(0 \le Ha \le 50\) ), the external Rayleigh number ( \(Ra_{E} = 10^{5}\) ), the parameter characterizing the intensity of heat generation ( \(R = 0\) and \(1\) ), and the power-law index ( \(0.8 \le n \le 1.2\) ). The findings of the present study are illustrated by presenting streamlines, isotherms, and mean Nusselt numbers.