The effect of equations of state on simulation of convective flow and heat transfer in near-critical liquids

Continuous media obeying an equation of state obtained within the mean-field model are treated in the vicinity of the critical point. This equation is an asymptotic approximation of an arbitrary two-parameter equation of state in which the first and the second derivatives of pressure with respect to density are zero and some other derivatives exist and are bounded. The thermodynamic relations, stratification, and characteristic time scales are obtained as functions of the coefficients in the equation of state. A numerical simulation is performed of convective flow and heat transfer in a square domain with side heat input; in so doing, approximate van der Waals and Redlich–Quong equations and an experimental relation are used as the equation of state. It is found that the simulation results agree qualitatively for all three cases.