Numerical study of free convection in an enclosure with two vertical isothermal walls

In this paper, natural convection is studied in a 2D-cavity with two vertical isothermal walls, kept at different temperatures, and two adiabatic walls which are either straight (rectangular cavity) or elliptic (modified rectangular cavity). The local mass, momentum and energy balance equations are written in a dimensionless form and solved numerically, by means of two different software packages based on Galerkin finite element methods. With reference to a Prandtl number of 0.71, two rectangular cavities are studied: a square one and a cavity with height double than width. Then, for each value of the ratio between height and width, two cavities with elliptic boundaries are investigated. The numerical solution shows that the elliptic boundaries enhance the mean Nusselt number and the dimensionless mean kinetic energy of the fluid