### Title : Magnetic field effects on Natural convection and Entropy Generation of non-Newtonian fluids using Multiple-relaxation-time lattice Boltzmann method

Authors : A. Rahman, P. Nag, M. M. Molla, S. Hassan

Abstract : In this paper, the magnetic field effect on natural convection of power-law non-Newtonian fluid is studied numerically by the multiple relaxation time (MRT) lattice Boltzmann method (LBM) in a two-dimensional enclosure. Numerical simulations have been done for Rayleigh number from \begin{math} Ra= 10^4 \end{math} to \begin{math} Ra= 10^6 \end{math}, Hartmann number from Ha = 0 to Ha = 20, power-law indices, $n$ = 0.6, 0.8, 1, 1.2 and 1.4, Prandtl number, $Pr$ = $6.2$ and aspect-ratio, $AR$ = 2 to study the temperature distributions and various flow patterns. The result shows that, Average Nusselt number is increased with the increase of Rayleigh number as well as power law index, and decrease with the increase of Hartmann number. Additionally, entropy generation for the non-Newtonian fluid is shown here. The study concludes that, with the absence of magnetic field, the all the entropy generation due to fluid friction, entropy generation due to heat transfer, entropy generation due to magnetic field, entropy and Bejan number decreases, whereas when the magnetic field is present, it rises until the fluid becomes Newtonian, and drops as soon as it becomes shear thinning. Moreover, comparison with the previous studies are discussed in detail. All simulations have been performed on Graphical Processing Unit (GPU) using NVIDIA CUDA for high computation performance.

 Journal : Journal of Modern Physics C Volume : Year : 2021 Issue : Pages : City : Edition : Editors : Publisher : ISBN : Book : Chapter : Proceeding Title : Institution : Issuer : Number :