Finite element simulation on MHD Free Convection in a Square Enclosure with Elliptical Shaped Obstacle

Abstract

The study is focused on the magneto-hydrodynamic (MHD) free convection flow phenomenon with varied positions of elliptical obstacle in a square enclosure. Cavity's base wall is uniformly heated, and the enclosure has a cold top wall and insulated side walls. Three diverse positions of elliptical obstacle, such as, left-bottom elliptical obstacle (LBEO), right-bottom elliptical obstacle (RBEO) and right-top elliptical obstacle (RTEO) are deemed for the analysis inside the enclosure. Additionally, the elliptical barriers are evenly heated. The mathematical model was created using a few governing equations with boundary conditions, and the non-dimensional governing equations were then solved using a Galerkin finite element formulation. Various elliptical obstacles and the parametric research study for the wide range of Hartmann number (0≤Ha≤100), fixed Rayleigh number (Ra = 103) and Prandtl number (Pr = 0.7) have been used in this case. The results have been demonstrated for various positions of elliptical obstacle (LBEO, RBEO and RTEO) using the streamline phase, isotherms, and average Nusselt number in the cavity. The average Nusselt number was found to drop for the pattern of LBEO and RBEO when the Hartman number was raised, but increased for RTEO pattern.

GANIT J. Bangladesh Math. Soc. 43.1 (2023) 063- 075