Finite element analysis of MHD natural convection within semi-circular top enclosure with a solid strip

Abstract

In this thesis, the problem of natural convection and heat transfer in a semi-circular top enclosure in presence of magnetic field with solid strip has been studied. The two-dimensional steady state Navier-stokes equations, energy equation and continuity equation are modified to account for the presence of thermal buoyancy and magnetic effects. The physical problems are represented mathematically by different sets of governing equations along with the corresponding boundary conditions. The equations are transformed to non-dimensional form with the help of suitable dimensionless variables. The dimensionless parameters appear in the equations are the Rayleigh number (Ra), Hartman number (Ha) and Prandtl number (Pr). The non-dimensional governing equations are solved by using Galerkin weighted residual method of finite element formulation. MHD free convection in a semi-circular top enclosure with different positions of a solid strip has been studied. All boundaries and solid strip are considered to be rigid. The left vertical wall and solid strip are maintained at hot temperature while the right wall is held at cold temperature. The semi-circular top and bottom walls are assumed to be adiabatic. Three different positions of solid strip namely horizontal, inclined and vertical are used in this thesis. Results are presented in terms of streamlines, isotherms, average Nusselt number along the heated left vertical wall, local Nusselt number along horizontal central line of the cavity or as required for different combinations of the non-dimensional governing parameters namely Rayleigh number (Ra) varying from 103 to 106, Hartman number (Ha) varying from 0 to 500 and Prandtl number (Pr) = 0.71. The range of Ra is selected on basis of calculation covering free convection dominated regimes. The computational results also indicate that the average Nusselt number at the heated left vertical wall of the cavity depends on the dimensionless parameters. Comparisons with previous published work are performed and the results are found to be in excellent agreement. The significant effect of the magnetic field is observed in the heat transfer mechanisms and flow characteristics inside the enclosure. With increasing of Hartmann number, flow velocity as well as heat transfer in the enclosure decreases. Vertical position of the solid strip in the enclosure gives the highest rate of heat transfer at Ra=106.