Heat conduction in a new Eulerian flow model

Abstract

M. Svärd has proposed the Eulerian flow model (EFM) [1] as a replacement for the traditional Navier–Stokes–Fourier (NS) equations. The EFM is equipped with a mass diffusion term in its mass balance law, along with other features, which lead to its satisfying the property of weak well-posedness in the special case of ideal gases with temperature-independent specific heats. Although this property is advantageous mathematically and numerically, it can be shown that the EFM fails to model certain types of problems physically. Here, as an example of the latter, steady-state problems of pure heat conduction are used to show that, when compared with predictions from Fourier’s law, the EFM substantially underestimates the magnitude of the heat flux in gases.