An example of entropy balance in natural convection,Part 2: the thermodynamic Boussinesq equations

Numerical simulations of natural convection performed with the usual Boussinesq equations result in unbalanced irreversibility budget. The thermodynamic Boussinesq equations solve this problem, especially because they simulate production of kinetic energy within the fluid through its expansion and contraction. These fluid volume changes, without which natural convection would not occur, also induce heat transfer by piston effect. The piston effect, which appears then as an intrinsic component of buoyancy-induced natural convection, introduces the non-dimensional adiabatic temperature gradient as a control parameter of natural convection. To cite this article: M. Pons, P. Le Quéré, C. R. Mecanique 333 (2005).