Numerical simulation of natural convection in a rectangular cavity with triangles of different orientation in presence of magnetic field

Abstract

Free convection flow and heat transfer in a rectangular cavity in presence of magnetic field with one heated side triangle in the enclosure is investigated numerically. A finite element analysis is performed to investigate the effects of uniform heating and is also used for solving the Navier-Stokes and Energy balance equations. The horizontal bottom wall is divided into three equal sections. The middle section of the horizontal bottom wall and one of the triangles in the enclosure were kept temperature at Th. The other two parts of the horizontal bottom wall and the other two sides of the triangle were kept thermal insulation while the left and right vertical walls and the top wall of the cavity were maintained constant temperature Tc with Th>Tc. The physical problems are represented mathematically by different sets of governing equations along with corresponding boundary conditions. The dimensionless Parameters in the equations are performed for magnetic parameter Hartmann number (Ha), Rayleigh number (Ra) and Prandtl number Pr. The streamlines, isotherms, average Nusselt number, velocity profiles and temperature distribution of the fluid in the enclosure are presented graphically. The numerical results indicate that the Hartmann number and Rayleigh number have strong influence on the streamlines and isotherms. Also the mentioned parameters have significant effect on average Nusselt number at the hot wall and average temperature of the fluid in the enclosure.