Lattice Boltzmann method to study free convection and entropy generation of power-law fluids under influence of magnetic field and heat absorption/generation

The aim of this present work assesses heat transfer and entropy generation arising from free convection of power-law fluids in a trapezoidal chamber under the effect of uniform and non-uniform magnetic field with heat absorption/generation by using LBM. The impact of Rayleigh number (10 3 , 10 4 and 10 5 ), wall slope (11.5°, 26.5° and 38.5°), power-law index (0.75, 1.0 and 1.25), Hartmann number (0, 15, 30 and 45), type of magnetic field applied (uniform and non-uniform) with heat absorption/generation (− 10, − 5, 0, + 5 and + 10) on fluid flow and heat transfer characteristics has been evaluated. By enhancement of the Rayleigh number and decreasing wall slope of the chamber, the flow strength, the rate of heat transfer and entropy generation increase and the effect of the magnetic field becomes more remarkable. By applying a magnetic field non-uniformly, the flow strength and heat transfer rate can be grown to about 25% and 15%, respectively. At higher Hartmann and Rayleigh numbers, the effect of changing the type of magnetic field applied is more notable. By increasing the heat absorption/generation coefficient, the average Nusselt number decreases and the effect of the magnetic field increases. In the heat generation mode, the total entropy generation increases with increasing Hartmann number, while in the heat absorption mode, the opposite effect was obvious. A salient and distinctive feature of the present work compared to previous studies is the application of non-uniform magnetic field (specific type of application) in the presence of heat absorption/generation for non-Newtonian fluids, which is not researched.