Flow of heat conducting fluid in a time dependent domain

TL;DR

This paper proves the existence of solutions for the heat conducting fluid flow governed by Navier-Stokes-Fourier equations in a moving, time-dependent domain with specific boundary conditions.

Contribution

It establishes the existence of variational solutions for the Navier-Stokes-Fourier system in a dynamic domain with full-slip boundary conditions.

Findings

Existence of variational solutions proven

Applicable to moving domains with prescribed shape changes

Addresses thermally isolated fluid conditions

Abstract

We consider a flow of heat conducting fluid inside a moving domain whose shape in time is prescribed. The flow in this case is governed by the Navier-Stokes-Fourier system consisting of equation of continuity, momentum balance, entropy balance and energy equality. The velocity is supposed to fulfill the full-slip boundary condition and we assume that the fluid is thermally isolated. In the presented article we show the existence of a variational solution.