Coupled Equations for Particle Velocity and Temperature Variation as the Fundamental Formulation of Linear Acoustics in Thermo-Viscous Fluids at Rest

This paper addresses a formulation of linear acoustics in thermo-viscous fluids at rest, in the form of a set of two equations for the temperature variation and the particle velocity. These variables are suitable to obtain explicit representation of the total perturbation field, because they are relevant to describe the scalar, potential acoustic and entropic movements, and the associated shear movement induced by viscosity effects. These variables are also relevant to derive boundary conditions, including both the thermal diffusion process through the interfaces between fluid and boundaries and the velocity field of these boundaries. This formulation offers analytical and numerical tools for solving most of the practical problems in thermo-viscous fluids (including thermo-viscous boundary layers) which was not available until now. In order to show the advantages and the efficiency of the formulation, a simple analytical solution is provided for the reflection of a plane wave, accounting for the viscous and thermal effects in the fluid and for thermal diffusion in the rigid wall boundary.