Magnetic field effects on natural convection and entropy generation of non-Newtonian fluids using multiple-relaxation-time lattice Boltzmann method

The magnetic field effect on natural convection flow of power-law (PL) non-Newtonian fluid has been studied numerically using the multiple-relaxation-time (MRT) lattice Boltzmann method (LBM). A two-dimensional rectangular enclosure with differentially heated at two vertical sides has been considered for the computational domain. Numerical simulations have been conducted for different pertinent parameters such as Hartmann number, Ha=0−20, Rayleigh number, Ra=104−106, PL indices, n=0.6–1.4, Prandtl number, Pr=6.2(water), to study the flow physics and heat transfer phenomena inside the rectangular enclosure of aspect-ratio AR=2.0. Numerical results show that the heat transfer rate, quantified by the average Nusselt number, is attenuated with increasing the magnetic field, i.e. the Hartmann number (Ha). However, the average Nusselt number is increased by increasing the Rayleigh number, Ra and decreasing the PL index, n. Besides, the generation of entropy for non-Newtonian fluid flow under the magnetic field effect has been investigated in this study. Results show that in the absence of a magnetic field, Ha=0, fluid friction and heat transfer irreversibilities, the total entropy generation decreases and increases with increasing n and Ra, respectively. In the presence of the magnetic field, Ha>0, the fluid friction irreversibility tends to decrease with increasing both the shear-thinning and shear thickening effect. It is noteworthy that strengthening the magnetic field leads to pulling down the total entropy generation and its corresponding components. All simulations have been performed on the Graphical Processing Unit (GPU) using NVIDIA CUDA and employing the High-Performance Computing (HPC) facility.