Mixed Magneto Convection in a Lid Driven Square Enclosure with a Sinusoidal Vertical Wall and Joule Heating

The problem of mixed convection flow in the presence of magnetic field in a lid-driven square cavity with a sinusoidal vertical wall and Joule heating were investigated numerically. The horizontal bottom and top walls are adiabatic. The left and right vertical walls are of temperature Th and Tc respectively with Th>Tc. The governing equations along with appropriate boundary conditions for the present problem are first transformed into a non-dimensional form and the resulting non linear system of partial differential equations are then solved numerically using Galerkin's finite element method. Parametric studies of the fluid flow and heat transfer in the enclosure are performed for magnetic parameter Hartmann number Ha, Joule heating J, Reynolds number Re and Richardson number Ri. The streamlines, isotherms, average Nusselt number at the hot wall and average temperature of the fluid in the enclosure are presented for the parameters. The numerical results indicate that the Hartmann number, Reynolds number and Richardson number have strong influence on the streamlines and isotherms. On the other hand, Joule heating parameter has little effect on the stream line and isotherm plots. Finally, the mentioned parameters have significant effect on average Nusselt number at the hot wall and average temperature of the fluid in the enclosure.