Similarity solutions of the entropy transport equation

Individual terms in the entropy transport equation are used today to analyse entropy production and dissipation within the flow. The underlying idea is that the local entropy production tells us where a particular design can be improved. However, very little attention has been paid up to now to the analysis of the full entropy transport equation. The present paper focuses on this topic and shows similarity solutions of the entropy transport equation. Two cases have been investigated as examples: laminar flow over a flat plate and flow between converging and diverging parallel plates, so called Jeffery–Hamel flows. Thus, similarity solutions have been derived for the boundary layer equations as well as for an analytical solution of the Navier–Stokes equations. These solutions show nicely the variation of all different terms in the entropy transport equation and highlight also restrictions under which such solutions can be obtained.