Relativistic heat conduction: the kinetic theory approach and comparison with Marle's model

TL;DR

This paper derives a relativistic heat flux closure from kinetic theory and compares it with Marle's BGK-like model, demonstrating improved accuracy in relativistic regimes over previous non-relativistic approximations.

Contribution

The work provides a kinetic theory-based derivation of relativistic heat flux relations and evaluates the effectiveness of Marle's model with relativistic correction factors.

Findings

Relativistic heat flux closure derived from kinetic theory.

Marle's model with correction factors shows good agreement in relativistic regimes.

Improved modeling of dissipative fluxes in relativistic hydrodynamics.

Abstract

In order to close the set of relativistic hydrodynamic equations, constitutive relations for the dissipative fluxes are required. In this work we outline the calculation of the corresponding closure for the heat flux in terms of the gradients of the independent scalar state variables: number density and temperature. The results are compared with the ones obtained using Marle's approximation in which a relativistic correction factor is included for the relaxation time parameter. It is shown how including such correction this BGK-like model yields good results in the relativistic case and not only in the non-relativistic limit as was previously found by other authors.