Thermomechanical coupling and second sound in superfluid flows

The present paper is concerned with the modelling of the influence of the thermomechanical coupling on the propagation of temperature waves (second sound) in superfluids. For an adequate heat transfer analysis in superfluids, finite thermal wave speed must be considered. Besides hyperbolic heat transfer, turbulent flows are generally observed despite the lost of internal friction. Due to the thermo-mechanical coupling, density waves may induce moving heat sources or sinks while temperature waves propagate at a different and independent speed. In particular, a rotational flow in this kind of fluid can strongly affect heat propagation. A general procedure, developed within the framework of thermodynamics of irreversible processes, is proposed to obtain constitutive relations that verify automatically the second law of thermodynamics and the principle of material objectivity. Such a phenomenological continuum approach allows a rational identification of the terms responsible for the thermomechanical coupling in the heat equation, which is a first step to better understand its influence on the superfluid flow.