On the Relaxation Time Scales of the Classical Thermodynamic Model for Heat Transfer in Quiescent Compressible Fluids

Abstract

An approximate solution of the classical thermodynamic model for compressible heat transfer of a quiescent supercritical fluid under microgravity leads to the wellknown piston effect relaxation time tPE=tD/(خ³0−1)2, where tD is the thermal diffusion relaxation time and خ³0 is the ratio between specific heats. This relaxation time represents an upper bound for the asymptotic bulk temperature behavior during very early times, which shows a strong algebraic relaxation due to the piston effect. This paper demonstrates that an additional relaxation time associated with the piston effect exists in this classical thermodynamic model, namely, tE=tD/خ³0. Furthermore, it shows that tE represents the time required by the bulk temperature to reach steadystate. Comparisons with a numerical solution of the compressible Navier–Stokes equations as well as experimental data indicate the validity of this new analytical expression and its physical interpretation.