From conduction to convection of thermally relativistic fluids between two parallel walls under gravitational force

TL;DR

This paper investigates the transition from thermal conduction to convection in thermally relativistic fluids between two walls under gravity, using theoretical assumptions and numerical simulations, revealing nonequilibrium states near the walls.

Contribution

It provides a numerical analysis of relativistic fluid behavior under gravity, highlighting the limitations of classical equations in transition regimes.

Findings

Strongly nonequilibrium states form near walls in relativistic fluids.

Transition from conduction to convection is hindered by nonequilibrium effects.

Nonrelativistic limits do not exhibit these nonequilibrium states.

Abstract

We discuss the thermal conduction and convection of thermally relativistic fluids between two parallel walls under the gravitational force, both theoretically and numerically. In the theoretical discussion, we assume that the Lorentz contraction is ignored and spacetime is flat. For understanding of the thermal conduction and convection of thermally relativistic fluids between two parallel walls under the gravitational force, we solve the relativistic Boltzmann equation using the direct simulation Monte Carlo method. Numerical results indicate that strongly nonequilibrium states are formed in vicinities of two walls, which do not allow us to discuss the transition of the thermal conduction to the thermal convection of thermally relativistic fluids under the gravitational force in the framework of the relativistic Navier-Stokes-Fourier equation, when the flow-field is under the transition regime between the rarefied and continuum regimes, whereas such strongly nonequilibrium states are not formed in vicinities of two walls under the nonrelativistic limit.