  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.
