Analytic solutions for the one-dimensional compressible euler equation with heat conduction and with different kind of equations of state

Abstract

We present analytic self-similar or traveling wave solutions for a one-dimensional coupled system of continuity, compressible Euler and heat conduction equations. Different kind of equations of state are investigated. In certain forms of the equation of state one can arrive to a picture regarding the long time behavior of density and pressure. The impact of these quantities on the evolution of temperature is also discussed. © 2013 Miskolc University Press.