Analysis of magnetohydrodynamic mixed convection and joule heating in lid-driven cavity having a square block

A numerical analysis is conducted to understand the effect of magnetic field and joule heating on the flow and thermal fields in a lid-driven cavity with a centered heat-conducting horizontal square block. The two sidewalls are maintained at uniform but different temperatures T(h) and T(c) (T(h) > T(c)), while the horizontal top and bottom walls are adiabatic. The left vertical wall moves up in the y-direction at a constant speed, while the other, walls remain stationary. An electrically conducting fluid is considered within the cavity. The physical problem is first represented mathematically by different sets of governing equations along with boundary conditions. A Galerkin weighted residual finite element method with a Newton-Raphson iterative algorithm is adopted to solve the governing equations along with the boundary conditions. The computation is carried out for wide ranges of Richardson numbers, magnetic parameter, joule heating parameter, and the size of the inner block. Results are presented in the form of streamlines, isothermal lines, average Nusselt number at the hot wall, and average fluid temperature in the cavity for the mentioned parameters. It is found that the flow field and temperature distribution strongly depend on magnetic parameter, joule heating parameter, and the size of the inner block at the pure mixed convection region.