Laminar natural convection in a square cavity: Low Prandtl numbers and large density differences

Steady natural convection at low Prandtl numbers caused by large density differences in a square cavity heated through the side walls is investigated numerically and theoretically. An appropriate dimensionless parameter characterizing the density differences of the working fluid is identified by the Gay-Lussac number. The Boussinesq assumption is achieved when the Gay- Lussac number tends to zero. The Nusselt number is derived for the ranges in Rayleigh number 10 6 Ra 6 108, in Prandtl number 0.0071 6 Pr 6 7.1 and in Gay-Lussac number 0 6 Ga < 2. The effects of the Rayleigh, Prandtl and Gay-Lussac numbers on the Nusselt number are discussed on physical grounds by means of a scale analysis. Finally, based on physical arguments, a heat transfer correlation is proposed, valid for all Prandtl and Gay-Lussac number ranges addressed.