Finite element analysis on magneto-hydrodynamic mixed convection flow in a triangular enclosure

Abstract

Combined effect of free and forced convection i.e. mixed convection occurs in many heat transfer devices, such as the cooling system of a nuclear power plant, large heat exchangers, cooling of electronic equipment, ventilation and heat or pollution agent clearance. In this thesis under the title “Finite Element Analysis on Magneto-hydrodynamic Mixed Convection Flow in a Triangular Enclosure”, two problems have been studied. The relative direction between the buoyancy force and the externally forced flow is important. In the case the fluid is externally forced to flow as the buoyancy force, the mode of heat transfer is termed combined forced and natural convection. The studies as well as depending on various flow and geometrical conditions are abstracted below. Initially, the effect of conduction in mixed convection flow in a triangular enclosure has been investigated numerically. The left vertical wall which is moving from the bottom corner of the cavity is kept at a uniform constant cold temperature and the bottom wall is heat generating, while the other inclined wall is assumed to be adiabatic or insulated. An external flow enters into the enclosure through the bottom portion of the left vertical wall. The fluid is concerned with Prandtl numbers 0.71, 2.0, 3.0 and 6.0. The properties of the fluid were presumed to be constant. The physical problems have been represented mathematically by different sets of governing equations along with the corresponding boundary conditions. The nondimensional 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 along the hot wall and average bulk temperature of the fluid in the cavity for different combinations of the governing parameters namely Reynolds number (Re), Prandtl number (Pr), Hartmann number (Ha) and Rayleigh number Ra, varying from 103 to 104. This range of Ra 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 hot wall of the cavity is depending on the dimensionless parameters. Comparisons with previously published work are performed and the results are found to be in excellent agreement. In conclusion, the consequences of conduction with magneto-hydrodynamics (MHD) mixed convection flow in a triangular enclosure have been investigated. The cavity consists of the same condition like previous one i.e. the effect of conduction in mixed convection flow in a triangular enclosure with left moving wall, adiabatic right inclined wall and heated bottom wall are considered. A uniform magnetic field is applied in the horizontal direction normal to the moving wall. Heat flow patterns in the presence of magnetic field within triangular enclosures have been analyzed with heatlines concept. The fluid is concerned with wide range of magnetic effect i.e. Hartmann numbers 5, 10, 20, 50 and Prandtl numbers 0.71, 2.0, 3.0, 6.0 at the three values of Rayleigh number Ra, varying from 103 to 104 which have been selected on the source of estimation of covering forced convection, mixed convection and free convection dominated regimes. Outcome of the numerical analysis has been presented in terms of streamline, isotherms, average Nusselt number and average bulk temperature along the heated bottom wall. The results indicate that both the flow and the thermal fields strongly depend on the parameters, Reynolds number (Re), Hartmann number (Ha), Prandlt number (Pr), at the convective regimes. It is also observed that the Prandtl number (Pr) influence on the flow field and have significant effect on the thermal field at the convective regimes. The computational results in both cases found that the flow and thermal field inside the cavity strongly depend on the relevant dimensionless numbers. For the purpose of comparison of the effect of MHD on heat transfer, the results in terms of average Nusselt number and average bulk temperature are shown in tabular form. The achieved results exposed that the effect of MHD has more influence than the case of without MHD on average Nusselt number and bulk temperature at the hot bottom wall.