Positivity of temperature for some non-isothermal fluid models

We establish three partial differential equation models describing the thermodynamic behavior of a fluid by combining the energetic variational approach, appropriate constitutive relations, and classical thermodynamic laws. By using an explicit algebraic approach, we show a maximum/minimum principle for some auxiliary variables involving the absolute temperature theta and density rho under some special conditions, which then yields the positivity of the temperature. This important fact implies the thermodynamic consistency for our models. (c) 2022 Elsevier Inc. All rights reserved.