Lattice Boltzmann Modeling for Natural Convection in Power-Law Fluids Within a Partially Heated Square Enclosure

This paper reports the numerical investigations for steady-state natural convection in power-law fluids inside a square enclosure embedded with bottom discrete heaters. The lattice Boltzmann method (LBM) is employed to model the flow and heat transfer phenomenon at different combinations of power-law index, Rayleigh number, and heat source length for a constant Prandtl number. The buoyancy force is incorporated in the collision term of the LBM through Boussinesq approximation. Simulation outcomes are furnished using streamlines, temperature contours, velocity profiles, and variation of heat transfer on the nonadiabatic walls to probe natural convection phenomena. The results indicate that the temperature and the flow fields in the enclosure are symmetric about the vertical centerline. The detailed physical interpretations have been provided for the reported results. Further, the increase in the power-law index means a rise in viscosity and a decrease in thermal energy transport for other constant parameters. The outcomes also specify that the intensity of circulation and heat transfer enhances with the increase of Rayleigh number and size of the localized heater. Finally, though, a rise in the size of the confined heat source enhances the rate of total thermal transport, it does not change the trend of fluid flow and local heat transfer rate.