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The present numerical study is devoted to investigate the mixed convection flow and heat transfer in a lid-driven cavity with wavy bottom surface. The cavity upper wall is moving with a uniform velocity by unity and the other walls are no slip. The cavity vertical walls are insulated while the upper surface is maintained at a uniform temperature higher than the wavy bottom surface. The physical problem is represented mathematically by a set of governing equations and the developed mathematical model is solved by employing Galerkin weighted residual method of finite element formulation. The wide ranges of governing parameters, i. e., the Reynolds number (Re), the Grshof number (Gr) and the number of undulations (λ) on the flow structure and heat transfer characteristics are investigated in detail. It is found that these parameters have significant effect on the flow fields; temperature distributions and heat transfer in the cavity. Furthermore, the trend of skin friction and Nusselt number for different values of the aforementioned parameters are presented in this investigation.

The effect of the Hall current on the magnetohydrodynamic (MHD) natural convection flow from a vertical permeable flat plate with a uniform heat flux is analyzed in the presence of a transverse magnetic field. It is assumed that the induced magnetic field is negligible compared with the imposed magnetic field. The boundary layer equations are reduced to a suitable form by employing the free variable formulation (FVF) and the stream function formulation (SFF). The parabolic equations obtained from FVF are numerically integrated with the help of a straightforward finite difference method. Moreover, the nonsimilar system of equations obtained from SFF is solved by using a local nonsimilarity method, for the whole range of the local transpiration parameter ζ. Consideration is also given to the regions where the local transpiration parameter ζ is small or large enough. However, in these particular regions, solutions are acquired with the aid of a regular perturbation method. The effects of the magnetic field M and the Hall parameter m on the local skin friction coefficient and the local Nusselt number coefficient are graphically shown for smaller values of the Prandtl number P r (= 0.005, 0.01, 0.05). Furthermore, the velocity and temperature profiles are also drawn from various values of the local transpiration parameter ζ.

In the present study the problem of mixed convection flow in the presence of magnetic field in a lid-driven square cavity with internal heat generation or absorption and uniform heating of bottom wall were investigated numerically. The square cavity vertical walls are maintained at cold temperature while the upper wall is insulated. The physical problem is then expressed mathematically by a set of governing equations and the developed mathematical model is solved by employing Galerkin weighted residual method of finite element formulation. Effects of variations of Richardson number, Hartmann number and heat generation or absorption parameter on flow structure and heat transfer rate (Nuesselt number) were studied in details. The significant reduction in the average Nusselt number were produced as the strength of the applied magnetic field was increased. In addition, heat generation predicted to decrease the average Nusselt number whereas heat absorption increases it.