This paper aims to present and then resolve the thermodynamic inconsistencies inherent in the usual Boussinesq model, especially with respect to the second law, and to highlight the effects of the correction.
The Boussinesq model (i.e. still assuming ▽v=0) is made thermodynamically consistent by maintaining in the heat equation, primarily the work of pressure forces, secondarily the heat generated by viscous friction. Numerically speaking, the modifications are very easy and hardly affect the computing time. However, new non‐dimensional parameters arise, especially the non‐dimensional adiabatic temperature gradient, ϕ.
There are presented and interpreted results of systematic numerical simulations done for a two‐dimensional square differentially‐heated cavity filled with air at 300K, with Rayleigh number ranging from 3,000 to 108 and ϕ ranging from 10−3 to 2. All configurations are stationary and the fluid is far from its critical state. Nevertheless, the pressure‐work effect (similar to the piston effect) enhances the heat transfer while diminishing the convection intensity. The magnitude of this effect is non‐negligible as soon as ϕ reaches 0.02.
The domain where the thermodynamic Boussinesq model must be used encompasses configurations relevant to building engineering.
Exact second‐law analyses can be developed with the so‐corrected model.
Pons, M. and Le Quéré, P. (2007), "Modeling natural convection with the work of pressure‐forces: a thermodynamic necessity", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 17 No. 3, pp. 322-332. https://doi.org/10.1108/09615530710730184
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