Finite element analysis of magnetohydrodynamic natural convection within semi-circular top enclosure with triangular obstacle of different orientation

Abstract

The phenomena of magneto-hydrodynamic natural convection in a two dimensional semicircular top enclosures with triangular obstacle in the rectangular cavity was studied numerically. The governing differential equations solved by using the most efficient method which is finite element method (weighted-residual method). Two-dimensional steady state Navier-Stokes equations, momentum equations, energy equation and continuity equation are calculatedwith magnetic effects. With proper selection 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 top wall is placed at cold Tc and bottom wall is heated Th. Here the sidewalls of the cavity assumed adiabatic. Also all the wall are occupied to be no-slip condition. A heated triangular obstacle is located at the center of the cavity. The study accomplished for Prandtl number Pr = 0.71, the Rayleigh number Ra = 103,105,5×105,106 and for Hartmann number Ha = 0,20,50,100. For the triangular obstacle three different rotation angles, namely (i) rotation angle 00(ii) rotation angle 300and (iii) rotation angle 900 are used in this investigation. The results are pictorial with the streamlines, isotherms, velocity and temperature fields as well as local Nusselt number 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. Evaluations with earlier published work have been executed and the results have 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. However, streamlines variation for different dimensionless numbers is noticeable a lot rather than temperature variation. The obtained results reveal that the temperature, heat transfer and fluid flow characteristics in the enclosure strongly depend on the relevant dimensionless set.