Thermodynamically Admissible Motion Past Rigid Obstacles With Isentropic or Nonisentropic Fluid–Solid Interfaces

Abstract

The motion of a fluid in a defined domain is called thermodynamically admissible if it satisfies the global system of the principles of balance of continuum mechanics and the principle of entropy or its equivalent differential system, consisting of differential equations and jump conditions. In an earlier publication, we have shown that the motion of a three-dimensional rigid body in an irrotational viscous and heat-conducting fluid violates the entropy jump condition, referred to as the Clausius–Duhem jump condition. Such a motion is thermodynamically inadmissible and could not persist. In a more recent publication, we have demonstrated that if the fluid–solid interface is isentropic, boundary conditions at a material interface, such as the no-slip condition and the continuity of the temperature, follow directly from the Clausius–Duhem jump condition. It is the purpose of this analysis to extend this methodology for the derivation of boundary conditions at isentropic material interfaces to nonisentropic material interfaces. We show that if the boundary conditions at the fluid–solid interface are a priori selected to satisfy the Clausius–Duhem jump condition, the resulting motion as described by the solution of the Navier–Stokes equations—whether the interface is isentropic or nonisentropic—is thermodynamically admissible.