FINITE ELEMENT ANALYSIS OF LAMINAR NATURAL CONVECTION IN A HEXAGONAL ENCLOSURE WITH INTERNAL RECTANGULAR BLOCKS

Abstract

Natural convection in enclosures with internal obstacles is relevant to electronic cooling, solar collectors and building ventilation. This paper studies steady, laminar, two-dimensional natural convection of a Boussinesq fluid in a hexagonal enclosure that contains four symmetrically placed rectangular blocks. The two lower inclined walls and the bottom wall are held at a hot temperature, the two upper inclined walls are cold, and the top wall is adiabatic. The continuity, momentum and energy equations are written in dimensionless form, which leaves the Rayleigh number  and the Prandtl number  as the governing parameters. The equations are solved with the finite element method using the Galerkin weighted residual formulation, implemented in COMSOL Multiphysics on a mesh of 17 066 elements. Streamlines, isotherms and temperature profiles are reported for ,  and  at , and for ,  and  at . At  and  the flow is weak and heat moves mainly by conduction. Raising  to  and , or raising  at , strengthens the circulation, bends the isotherms around the blocks, compresses them towards the cold walls and produces a nearly isothermal core. The temperature gradient is largest at  and varies non-monotonically with .