Natural convection in a 2D-cavity with vertical isothermal walls: cross-validation of two numerical solutions

In this paper, a numerical study of natural convection in a 2D-enclosure is presented. The enclosure is bounded by two vertical isothermal walls, kept at different temperatures, and by two adiabatic walls which are either straight and horizontal (rectangular cavity) or elliptic (modified rectangular cavity). The dimensionless mass, momentum and energy balance equations are solved by means of two different software packages based on Galerkin finite element methods. An excellent agreement between the solutions is found and provides a cross-validation of the results. Two basic geometries are considered: a square geometry and a rectangular one with height double the width. For each basic geometry, three cavities are investigated: a rectangular cavity, and two modified rectangular cavities. Dry air is considered, with several values of the Rayleigh number. The results show that the elliptic boundaries enhance the mean Nusselt number and the dimensionless mean kinetic energy of the fluid