Analytic solutions for the one-dimensional compressible Euler equation with heat conduction closed with different kind of equation of states

TL;DR

This paper derives analytic self-similar and traveling wave solutions for a 1D coupled system of Euler and heat conduction equations with various equations of state, analyzing long-term behavior of density, pressure, and temperature.

Contribution

It provides new analytic solutions for the coupled Euler and heat conduction system under different equations of state, enhancing understanding of their long-term dynamics.

Findings

Long-term behavior of density and pressure analyzed

Impact of equations of state on temperature evolution discussed

Analytic solutions derived for various state equations

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 equation of states 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.