Numerical Study of Magnetohydrodynamic Free Convection in a Rectangular Cavity with Corner Heater Having a Triangular Obstacle

Abstract

This study explores the numerical investigation of magnetohydrodynamic free convection flow within a rectangular cavity featuring a triangular obstacle near a corner heater. The upper horizontal wall is maintained at a cool temperature, while the right bottom corner is heated, and the remaining walls are kept adiabatic. Solving the governing nonlinear differential equations for general flow problems, along with boundary conditions, is accomplished using the Galerkin weighted residual finite element method. The simulation spans a broad range of parameters, including Rayleigh number , Hartmann number , and Prandtl number  Results are presented in terms of stream functions, temperature profiles, and Nusselt Numbers. At low Rayleigh numbers , the isotherms exhibit near-parallel alignment with the upper portion of the triangular obstacle, while higher  values lead to more distorted isotherms. An increase in Rayleigh number corresponds to a significant enhancement in flow circulation and heat transfer. Isotherms distributions remain consistent with increasing Hartmann numbers, but higher Hartmann numbers influence streamlines. Validation of the numerical model against previously published results demonstrates good agreement.