Magnetohydrodynamic Mixed Convection in a Vertical Rectangular Cavity with Semi-circular Heat Source and Circular Obstacle

Abstract

A study of MHD mixed convection in a vertical rectangular cavity with semi-circular heat source and circular obstacles is accomplished numerically. A semi-circular heat source is placed at the middle of the bottom wall of the cavity and the top wall of the cavity is kept isothermally cooled while other walls are considered adiabatic. Moreover, a hollow circular cylinder is also placed as an obstruction at the center of the cavity. Finite element method is applied to determine a numerical solution of the non-linear coupled equations. Computations have been carried out for the flow and thermal fields inside the cavity which inclusively depends on the applied magnetic field parameter called Hartmann number (Ha) and other dimensionless numbers such as Reynolds number (Re), Richardson number (Ri) and Prandtl number (Pr). From this analysis it is observed that the fluid flow in the cavity is noticeably slowed down by the increase in Ha, heat transfer rate is significantly increased for increasing Re and Ri, but it decreased for increasing the values of Pr and Ha. In addition, the average temperature within the cavity shows opposite behaviors for variations in physical parameters studied except for Ha.