MHD mixed convection flow around a triangular obstacle placed in a lid driven square cavity

Abstract

Combined free and forced convective flow in lid driven cavities occurs as a result of two competing mechanisms. The first one is due to shear flow caused by the movement of one of the walls of the enclosure, while the following one is due to buoyancy flow produced by thermal non-homogeneity of the enclosure boundaries. Analysis of mixed convective flow in a lid-driven enclosure finds applications in material processing, flow and heat transfer in solar ponds, dynamics of lakes, reservoirs and cooling ponds, crystal growing, float glass production, metal casting, food processing, galvanizing, and metal coating. In this thesis under the title “MHD mixed convection flow around a triangular obstacle placed in a lid driven square cavity” all mechanisms of convection such as natural, mixed and forced convection have been studied. The relative direction between the buoyancy force and the externally forced flow is important. In the case where the buoyancy force and external force both are present, the flow is termed as mixed convection. The studies as well as dependence on various non-dimensional parameters and geometrical conditions are abstracted below. Initially, numerical simulation of two-dimensional laminar steady-state heat line concept for MHD mixed convection within square cavity has been investigated. In this study, mixed convection within a square cavity for heated bottom wall, adiabatic top wall and cold side walls containing a centered triangular obstacle of different area is considered. Heat flow patterns in the presence of mixed convection within square enclosure have been analyzed with heat lines concept. The fluid is concerned with various values of Hartmann number; Ha= 0, Ha= 20, Ha= 40, Ha= 60, Prandtl number; Pr= 0.03, Pr=0.71, Pr=2.56, Pr=5.43 with various triangular obstacle areas as A=0, A=0.03, A=0.08 and A=0.125. The properties of the fluid are presumed to be constant. The physical problems are represented mathematically by different sets of governing equations along with the corresponding boundary conditions. The non-dimensional governing equations are discretized by using Galerkin weighted residual method of finite element formulation. Results are presented in terms of streamlines, isotherms, average Nusselt number with along the heated wall of square cavity, local Nusselt number with along the bottom wall of square cavity, local Nusselt number along the bottom wall of triangular obstacle. Results are also presented through different figures of Richardson number vs Nusselt number, Richardson number vs temperature for different combinations of the governing parameters namely Prandtl number Pr, Hartmann number Ha, obstacle area A and at the five values of Richardson number Ri=0.1, Ri=0.5, Ri=1, Ri=5 and Ri=10. This range of Ri is selected on the basis of calculation covering forced convection, mixed convection and free convection dominated regimes. The computational results also indicate that the average Nusselt number at the heated wall of the cavity and triangular obstacle depends on the dimensionless parameters. Comparisons with previously published work are performed and the results are found to be in excellent agreement.