Finite Element Analysis of MHD Natural Convection in a Rectangular Cavity and Partially Heated Wall

In this paper numerical study is presented of two-dimensional laminar steady-state on megneto-hydrodynamics (MHD) free convection for heat flow patterns within rectangular enclosures. A finite element analysis is performed to investigate the effects of uniform heating and is also used for solving the Navier-Stokes and Energy balance equations. The horizontal bottom wall is divided into three sections. The middle section of the horizontal bottom wall was kept temperature at T h and the other two parts of the horizontal bottom wall were kept thermal insulation while the left and right vertical walls and the top wall of the cavity were maintained constant temperature Tc with T h >T c . Parametric studies of the fluid flow and heat transfer in the enclosure are performed for magnetic parameter Hartmann number (Ha = 0, 50, 100), Rayleigh number (Ra = 10 3 – 10 6 ) and Prandtl number Pr=0.71. The streamlines, isotherms, average Nusselt number at the hot wall and velocity profiles and temperature distribution of the fluid in the enclosure are presented for the parameters. The numerical results indicated that the Hartmann number and Rayleigh number have strong influence on the streamlines and isotherms. Also the mentioned parameters have significant effect on average Nusselt number at the hot wall and average temperature of the fluid in the enclosure.