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

A study of MHD mixed convection in a vertical rectangular cavity with semi-circular heat source and circular obstacle 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, Ri and Pr but it decreased for increasing the values and Ha . It is also numerically observed that heat transfer rate increases by 762.20% and 727.26% for varying Re from 10 to 500 at Ha = 0 and Ha = 10 which is reduced to 315.69% at Ha = 50. Moreover, heat transfer rate is increased by 150.09% and 547.21% while Ri varies from 0.01 to 10 and Pr varies from 0.03 to 13.6, respectively at Re = 100. In addition, the average temperature within the cavity exhibited the opposite behavior for variations in physical parameters studied except for Ha .