Effect of an ascendant magnetic field on Rayleigh-Benard convection for non-Newtonian power-law fluids in a horizontal rectangular cavity submitted to vertical temperature gradient

We approach the effect of an external magnetic field on induced natural convection flows within a horizontal rectangular cavity heated from below and containing electrically conducting non-Newtonian fluids. The vertical walls of this cavity are assumed to be insulated. The rheological behavior of the fluids considered is modeled by the power-law of Ostwald-De-Weale. The centered finite difference method is used to solve the governing equations. The parameters on which this problem depends are the aspect ratio of the cavity, A, the Rayleigh number, Ra, the Prandtl number, Pr, the fluid behavior index, n and the Hartmann number, Ha. The effect of magnetic field, rheology and their interaction on flow and heat transfer is examined and discussed in detail.