A numerical study of natural convection in an inclined square enclosure with an elliptic cylinder using variational multiscale element free Galerkin method

Abstract In this paper, a numerical study for steady-state natural convection in a cold outer square enclosure containing a hot inner elliptic cylinder is investigated using the variational multiscale element free Galerkin method (VMEFG). The VMEFG method is a meshless method which coupled element free Galerkin method and variational multiscale method, it allows equal order basis for the velocity and the pressure field. The numerical calculations are performed for various Rayleigh numbers ranging from 10 3 to 10 6 , the inclination angle of the outer square enclosure from 0° to 45° and major axis of the inner cylinder from 0.2 L to 0.4 L. The results show that the Rayleigh number, the size of the inner cylinder and the inclination angle of the outer square enclosure have remarkable effects on the streamlines and temperature contours in the enclosure, but the inclination angle of the enclosure has a small effect on average Nusselt number on the inner elliptic cylinder.