Finite element simulation of mhd mixed convection in a rectangular cavity containing heated block and two semi-circular wall heater

Abstract

Mixed 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 the buoyancy flow produced by thermal non-homogeneity of the enclosure boundaries. Analysis of mixed convective flow in a lid-driven enclosure finds application 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 all mechanisms of convection such as natural, mixed and forced convection have been studied. The relative direction between the buoyancy force and the externally imposed flow is important. In the case where the buoyancy force and external force both are present termed as mixed convection flow. This study depends on various non-dimensional parameters and geometrical conditions which are abstracted below. A numerical simulation of two dimensional laminar steady flow for MHD mixed convection within rectangular cavity with two semi-circular wall heater and heated block in the middle has been performed. Two different shapes of heated block i.e. trapezoidal and rectangular has been considered. Present study consists a concentrated heated block in the middle and two concentrated semi-circular wall heater, adiabatic upper and bottom wall except two semi-circular wall heater, left and right cold and low concentrated wall and moving upper wall. The fluid is concerned with various values of Hartmann number; Ha=0,Ha=50,Ha=100 and Ha=150, Richardson number ; Ri=0.1,Ri=1,Ri=5 and Ri=10, buoyancy ratio; Br=2, Br=5, Br=10 and Br=20 with different shapes of heated and concentrated obstacle areas as A=0.042 and A=0.028. Also the value of Prandtl number; Pr=7 and Lewis number; Le=2 have been kept fixed in the present study. 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. Numerical simulation results are presented in terms of streamlines, isotherms, average Nusselt number along with the left and right semi-circular wall. We also plotted average Nusselt number Vs Richardson number for different shaped obstacle along the two semi-circular wall heater with MHD and without MHD, average Nusselt number Vs Richardson number for different values of Ha along the two semi-circular wall heater with trapezoidal and rectangular obstacle and average Nusselt number Vs Richardson number along the two semi-circular wall for different values of Br with MHD for trapezoidal and rectangular obstacle. The range of Richardson number is selected on the basis of calculation covering forced, mixed and free convection dominated regions. The computational results indicate that the average Nusselt number at the two semi-circular wall depends on the dimensionless parameters and the shapes of obstacle. Comparison with previously published work are presented and the results are found to be in excellent agreement.