Effect of a heat conducting horizontal circular cylinder on MHD mixed convection in a lid-driven cavity along with joule heating

Magnetohydrodynamic (MHD) mixed convection in a liddriven cavity along with joule heating is studied numerically. The cavity consists of adiabatic horizontal walls and differentially heated vertical walls, but it also contains a heat conducting horizontal circular cylinder located somewhere within the cavity. The aim of the study is to delineate the effect of such a cylinder on the flow and temperature fields. The governing equations are first transformed into a non- dimensional form and resulting nonlinear system of partial differential equations are then solved by using Galerkin weighted residual method of finite element formulation. The analysis is conducted by observing variations of the streamlines and isotherms for the size, locations and thermal conductivity of the cylinder at the Richardson number Ri ranging from 0.0 to 5.0, Prandtl number Pr = 0.71 and Reynolds number Re = 100 with constant physical properties. The results indicated that both the streamlines and isotherms strongly depend on the size and locations of the inner cylinder, but the thermal conductivity of the cylinder has significant effect only on the isothermal lines. The variations of average Nusselt number on the hot wall and average fluid temperature in the cavity are also presented to show the overall heat transfer characteristics inside the cavity