Numerical study on the conjugate effect of joule heating and magnato-hydrodynamics mixed convection in an obstructed lid-driven square cavity

Conjugate effect of joule heating and magnetic force, acting normal to the left vertical wall of an obstructed lid-driven cavity saturated with an electrically conducting fluid have been investigated numerically. The cavity is heated from the right vertical wall isothermally. Temperature of the left vertical wall, which has constant flow speed, is lower than that of the right vertical wall. Horizontal walls of the cavity are adiabatic. The physical problem is represented mathematically by sets of governing equations and the developed mathematical model is solved by employing Galerkin weighted residual method of finite element formulation. To see the effects of the presence of an obstacle on magnetohydrodenamic mixed convection in the cavity, we considered the cases of with and without obstacle for different values of Ri varying in the range 0.0 to 5.0. Results are presented in terms of streamlines, isotherms, average Nusselt number at the hot wall and average fluid temperature in the cavity for the magnetic parameter, Ha and Joule heating parameter J. The results showed that the obstacle has significant effects on the flow field at the pure mixed convection region and on the thermal field at the pure forced convection region. It is also found that the parameters Ha and J have notable effect on flow fields; temperature distributions and heat transfer in the cavity. Numerical values of average Nusselt number for different values of the aforementioned parameters have been presented in tabular form.