Effect of Prandtl Number on Magneto- Convection in a Lid Driven Square Cavity with a Sinusoidal Vertical Wall

In the present study the effect of Prandtl number on magneto-convection in a lid driven square cavity with a sinusoidal vertical wall were investigated numerically. The horizontal bottom and top walls are adiabatic. The left and right vertical walls are 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 Prandtle number Pr, Reynolds number Re. and sinusoidal λ. The streamlines, isotherms, average Nusselt number at the hot wall and average temperature of the fluid in the enclosure are presented. The numerical results indicate that the Reynolds number has strong influence on the streamlines and isotherms. On the other hand, Prandtl number and undulation λ have 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. Keywords—Prandtlnumber, Magnetohydrodynamic, Finite element method, Mixed convection and Lid driven enclosure