Stationary Couette-type flows in relativistic fluids

TL;DR

This paper studies stationary relativistic fluid flows between parallel plates, highlighting the importance of heat flux in accurately modeling flow profiles due to relativistic effects like heat inertia.

Contribution

It demonstrates that neglecting heat flux yields incorrect flow profiles in relativistic fluids, emphasizing the role of heat inertia in such systems.

Findings

Heat flux significantly affects flow profiles in relativistic fluids.

Neglecting heat flux leads to qualitatively incorrect results.

Heat inertia is crucial in the Landau frame for relativistic flows.

Abstract

We investigate a class of stationary, planar-symmetric solutions of relativistic hydrodynamics, in which a dissipative fluid is confined between two parallel plates that move relative to each other and/or are maintained at different temperatures. We find that neglecting the heat flux leads to qualitatively incorrect flow profiles, even in systems with temperature-independent viscosity. This arises from the fact that, in special relativity, the heat flux itself contributes to the momentum density (the so-called "inertia of heat"). This effect is most evident in the Landau frame, where the fluid removes the excess energy generated by viscous heating by streaming across the boundaries. The analysis is further extended to the limit of vanishing chemical potential.