Abstract:
Free convection flow and heat transfer in a square cavity in the presence of magnetic field with semicircular block is studied. The physical problems are represented mathematically by different sets of governing equations along with the corresponding boundary conditions. For this, 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. With proper choice of the dimensionless variables, the equations are transformed to non-dimensional form. The dimensionless parameters appear in the equations are the Rayleigh number (Ra), Hartmann number (Ha) and Prandtl number (Pr). The equations are solved numerically by finite element method using Galerkin weighted residual approach. The non linear algebraic equations obtained from the differential equation are solved by Newton-Raphson method. In this thesis MHD free convection in a square cavity with different rotations of semicircular block has been studied. All four boundaries of the square cavity and semicircular block are considered to be rigid. The bottom wall and semicircular block are maintained at hot temperature while the top wall is held at cold temperature. The left and right walls are assumed to be adiabatic. For the semicircular block three different rotation angles, namely (i) rotation angle 0o (ii) rotation angle 60o and (iii) rotation angle 90o are used in this thesis. Results are presented in terms of streamlines, isotherms, average Nusselt number along the heated bottom wall, Local Nusselt number along horizontal and vertical lines for different combinations of the non-dimensional governing parameters namely Hartmann number Ha varying from 0 to 100 and Rayleigh number Ra, varying from 103 to 106. This range of Ra is selected on the basis of calculation covering free convection dominated regimes. The computational results also indicate that the average Nusselt number at the heated bottom wall of the cavity depends on the dimensionless parameters. Comparisons with previously published work are performed and the results are found to be in excellent agreement. The temperature of the fluid in the cavity decreases due to the increase of the Rayleigh number, consequently the rate of heat transfer from the bottom wall increases.
The significant effect of the magnetic field is observed in the heat transfer mechanisms and flow characteristics inside the cavity. Strong suppression of the convective current can be obtained by applying strong magnetic field. This is why; reductions in the average Nusselt number were produced as the strength of the applied magnetic field were increased. The obtained results reveal that the temperature, heat transfer and fluid flow characteristics in the cavity strongly depend on the relevant dimensionless set. Increase in rotation angle of semicircular block enhance heat transfer rate.
