Positivity of temperature for some non-isothermal fluid models

TL;DR

This paper develops PDE models for non-isothermal fluids, demonstrating temperature positivity through maximum/minimum principles, ensuring thermodynamic consistency of the models.

Contribution

It introduces new PDE models for non-isothermal fluids and proves temperature positivity using an algebraic maximum/minimum principle, ensuring thermodynamic consistency.

Findings

Established PDE models for thermodynamics of fluids.

Proved temperature positivity under certain conditions.

Ensured thermodynamic consistency of the models.

Abstract

We establish three partial differential equation models describing the thermodynamics of the fluid, by combining the energetic variational approach, appropriate constitutive relations, and classical thermodynamics laws. What is more, by using a clear algebraic approach, we show a maximum/minimum principle for some quantities composed by the absolute temperature $\theta$ and density $\rho$ under some special conditions, which in turn gives the positivity of the temperature. This important fact implies the thermodynamic consistency for our models.