Optimal wall natural convection for a non-Newtonian fluid with heat generation/absorption and magnetic field in a quarter-oval inclined cavity

Abstract

Abstract For the first time, the present work investigates natural convection heat transfer in a two-dimensional inclined quarter-oval cavity filled with a non-Newtonian power-law fluid with heat generation/absorption in the presence of a magnetic field using the Lattice Boltzmann Method (LBM). Part of the vertical wall of the cavity is maintained at a constant hot temperature while the curved wall is kept at a constant cold temperature. All other walls are maintained adiabatic. The effect of physical parameters such as the Hartmann number, non-Newtonian power-law fluid index, heat generation/absorption coefficient and the inclination angle of the cavity on the nature of flow and heat transfer is studied and analyzed. The present work is validated with previous studies and the results are in very good agreement. The obtained results show that increasing the power-law fluid index on the average reduces the maximum value of the streamlines by 88% and the average Nusselt number by 45%. Also, increasing the Hartmann number reduces the heat transfer from the wall to the fluid. In the case of heat absorption and heat generation, the average Nusselt number is about 30% higher and 55% lower than in the case where there is no heat absorption/production, respectively. In addition, heat generation on the average increases the fluid flow power by 15%, which is negligible for the shear thickening fluid case. By increasing the heat generation/absorption coefficient and decreasing the non-Newtonian power-law fluid index, the effect of the magnetic field increases. The lowest amount of heat transfer is observed at a 90 degrees inclination angle of the cavity for which the average Nusselt number is up to about 10% less in this case. In the absence of a magnetic field and at a 180 degrees inclination angle, the maximum amount of heat transfer from the wall to the fluid is observed for a non-Newtonian shear thinning fluid and for heat absorption. This study could pave the way for the optimal design of industrial thermal equipment.