1. Entropy equation

In a fluid, stresses are essentially due to hydrostatic pressure p. The mechanical tension T exerted on each surface element is almost normal to it. A deviation from this law occurs with viscosity, which creates tangential stresses τ _ij . To separate the two effects, let's take the stress tensor as :

with δ _ij Kronecker symbol.

The viscous stresses τ _ij lead to the dissipation of part of the mechanical energy. The evolution...