High Gradient Temperature Thermo-Buoyant Flow in a Square Cavity with Magnetoconvection Using a Novel Non-Boussinesq Algorithm

Abstract

We study numerically the heat transfer of steady laminar flow in a square cavity filled with electrically conducting fluids, in the presence of an external uniform magnetic field. Imposing a large temperature gradient between two opposite vertical walls, there are substantial temperature and density variations in the domain. The fluid is treated as an ideal gas. Indeed, high temperature gradient thermo-buoyant cavity flows result in natural convection flow domains with high Rayleigh number. To implement the temperature variation effect, the fluid properties, including the conductivity and viscosity coefficients, are considered to vary with temperature in accordance to the Sutherland's law. We use a novel non-Boussinesq algorithm to include the density variation in the domain. Of importance, the current results are different from those obtained considering the classical Boussinesq assumption, in which the density variation is replaced with the temperature variation. We use the finite volume method and SIMPLE algorithm to treat the continuity, momentum, and energy equations. The results show that the magnetic field plays a damping role in the flow pattern formations. We show that the increase of Hartmann number would decrease the maximum fluid velocity and Nusselt number magnitudes. Generally, the current study indicates that the computational heat transfer applicants, who need to take into account the effect of MHD in high thermobuoyant flow field treatments, should consider a variable density instead of using the classical Boussinesq approximation if they wish to achieve accurate solutions; specifically in higher Rayleigh number regime applications.