Numerical investigation of heat transfer in a power-law non-Newtonian fluid in a C-Shaped cavity with magnetic field effect using finite difference lattice Boltzmann method

The present study aimed to investigate the natural convection heat transfer in a power-law, non-Newtonian fluid under an applied magnetic field inside a C-shaped cavity using the Finite Difference Lattice Boltzmann method (FDLBM). Temperature distribution on the wall on the left side was non-uniform and sinusoidal with the cold wall on the right side. Both top and bottom horizontal walls of the cavity were insulated against heat and mass transfer. The Boussinesq approximation was used due to negligible density variations, making the hydrodynamic field sensitive to the thermal field. Furthermore, the D2Q9 lattice arrangement was used for the density and energy distribution functions‏. This study investigates the effects of the Rayleigh number, exponential function index, aspect ratio, and the Hartmann number on the flow and temperature fields. The results show that the heat transfer rate increases with increasing Rayleigh number. Moreover, it was found that the Nusselt number decreases with increasing power-law index (n) at higher Rayleigh numbers and that an increase in the Hartmann number results in a reduced heat transfer rate. The reduction in the heat transfer rate caused by the increased Hartmann number in the shear thinning fluids was more than that in shear thickening fluids. The Nusselt number decreases with increasing cavity aspect ratio for the Newtonian and shear thinning fluids, whereas for shear thickening fluids, the Nusselt number initially increased and then decreased.