Anomalous heat transport by the piston effect in supercritical fluids under zero gravity

Fast heat transfer calculations in supercritical fluids versus hydrodynamic approach

“…is replaced by p (1) for the sake of compactness. The pressure term p (1) has to be interpreted as the dynamic pressure that makes the velocity field satisfy the continuity equation (29).…”

“…The pressure term p (1) has to be interpreted as the dynamic pressure that makes the velocity field satisfy the continuity equation (29). This term reflects the contribution of the acoustic waves averaged over several wave periods to the total pressure field.…”

“…After several sound wave periods the pressure is already equilibrated and can be assumed to be nearly homogeneous along the cavity. During the initial stage of heating, this process of energy transfer, called "Piston effect" [1,2], is much more efficient than the usual diffusion scenario. Indeed, if the Piston effect were absent, the bulk of the fluid would remain at the initial temperature.…”

“…This consists in calculating the temperature in the whole fluid volume using Eqs. (1)(2) for some trial value of p (and thus ∂p/∂t) and determining the other thermodynamic parameters (ρ, χ T , . .…”

“…(3). Teams with expertise in theoretical hydrodynamics have developed a rigorous hydrodynamic approach [1] in which the Navier-Stokes and energy equations are coupled with the EOS. This set of equations has been solved analytically in 1D by asymptotic matching techniques [9] and also by direct numerical simulation (DNS) [10] via the finite volume method [11] both in 1D and 2D.…”