Hydro-magnetic mixed convection in a lid-driven cavity with partially thermally active walls

In most of the studies, either the study on mixed convection in a square cavity with isothermal vertical walls or study on natural convection in a square cavity with partially thermally active walls have been considered. To best of our knowledge, mixed convection in a square cavity with partially thermally active side walls is not reported so far. Moreover, the effects of partial heating/cooling on mixed convection are important especially in the cooling of electronic equipments. So, the main aim of the present chapter is determining the optimum location of the heating and cooling regions on respective vertical walls in mixed convection with different internal heat generation or absorption parameters. 6. 2 Mathematical formulation Unsteady, laminar, incompressible combined convective flow and heat transfer in a two dimensional square cavity of size L filled with air is considered. The physical model and the coordinate system considered in this investigation are shown in Figure 6.1(a). The Cartesian coordinates (x, y) with the corresponding velocity components (u, v) are also indicated in the Figure 6.1(a). The top wall of the cavity is allowed to move in its own plane at a constant speed 0 U. A portion of the left and right walls are kept at constant temperatures H T and C T , with C H T T , respectively. The left and right portions of walls are regarded as heating and cooling regions, respectively. The constant length of region(s) is considered to be L/2. The remaining portions of the left and right walls, top and bottom walls of the cavity are insulated. Five different combinations of location are taken into account to place the regions on their respective walls. When both the heating and cooling regions are located at top of their respective walls, the combination is considered to be Top-Top case. Similarly, Middle-Middle, Bottom-Bottom, Bottom-Top and Top-Bottom are deliberated in the remaining cases according to the location of regions. The cases are clearly shown in Figure 6.1(b). The gravity acts in the negative y-direction. The thermo-physical properties of the fluid are assumed to be constant, except the density in the buoyancy term.