Heat Flux for a Relativistic Dilute Bidimensional Gas

García‐Perciante, A. L.; Méndez, A. R.; Escobar-Aguilar, Eric S.

doi:10.1007/s10955-017-1742-x

Cited by 12 publications

(17 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The calculation follows somewhat closely the one carried out in Ref. [10] and the reader is referred to such publication for further details. By direct inspection one notices that the integral equations (35) and (37) have the same structure and thus only the first one needs to be solved.…”

Section: The Vector Equation and The Heat Fluxmentioning

confidence: 76%

Dissipative properties of relativistic two-dimensional gases

García‐Perciante

Méndez

2019

Physica A: Statistical Mechanics and its Applications

View full text Add to dashboard Cite

The constitutive equations for the heat flux and the Navier tensor are established for a high temperature dilute gas in two spatial dimensions. The Chapman-Enskog procedure to first order in the gradients is applied in order to obtain the dissipative energy and momentum fluxes from the relativistic Boltzmann equation. The solution for such equation is written in terms of three sets of orthogonal polynomials which are explicitly obtained for this calculation. As in the three dimensional scenario, the heat flux is shown to be driven by the density, or pressure, gradient additionally to the usual temperature gradient given by Fourier's law. For the stress (Navier) tensor one finds, also in accordance with the three dimensional case, a non-vanishing bulk viscosity for the ideal monoatomic relativistic two-dimensional gas. All transport coefficients are calculated analytically for the case of a hard disk gas and the non-relativistic limit for the constitutive equations is verified.

show abstract

Section: The Vector Equation and The Heat Fluxmentioning

confidence: 76%

Dissipative properties of relativistic two-dimensional gases

García‐Perciante

Méndez

2019

Physica A: Statistical Mechanics and its Applications

View full text Add to dashboard Cite

show abstract

“…In spite of its importance, a robust methodology connecting kinetic and hydrodynamic parameters in (2+1)dimensions is still lacking; Mendoza et al [60] derived transport coefficients for an ultra-relativistic ideal gas using Grad's method of moments and the relaxation time approximation (RTA) while, to the best of our knowledge, the Chapman-Enskog expansion has not been fully derived, with only one calculation of thermal conductivity available in literature [61].…”

Section: Introductionmentioning

confidence: 99%

Relativistic dissipation obeys Chapman-Enskog asymptotics: Analytical and numerical evidence as a basis for accurate kinetic simulations

et al. 2019

View full text Add to dashboard Cite

We present an analytical derivation of the transport coefficients of a relativistic gas in (2 + 1) dimensions for both Chapman-Enskog (CE) asymptotics and Grad's expansion methods. We further develop a systematic calibration method, connecting the relaxation time of relativistic kinetic theory to the transport parameters of the associated dissipative hydrodynamic equations. Comparison of our analytical results and numerical simulations shows that the CE method correctly captures dissipative effects, while Grad's method does not, in agreement with previous analyses performed in the (3 + 1) dimensional case. These results provide a solid basis for accurately calibrated computational studies of relativistic dissipative flows.

show abstract

“…in [27] by introducing BGK-like relaxation approximations for the collision operator and considering the Jttner distribution function for the equilibrium state. Whereas in [28], the constitutive equation for the heat flux and the corresponding thermal conductivity were obtained for a nondegenerate gas by using the complete collision term of the 2D relativistic Boltzmann equation within the wellknown Chapman-Enskog method.…”

Section: Introductionmentioning

confidence: 99%

Thermal Dissipation in Two Dimensional Relativistic Fermi Gases with a Relaxation Time Model

2020

Self Cite

View full text Add to dashboard Cite

The thermal transport properties of a two dimensional Fermi gas are explored, for the full range of temperatures and densities. The heat flux is established by solving the Uehling-Uhlebeck equation using a relaxation approximation given by Marle's collisional kernel and considering the temperature and chemical potential gradients as independent thermodynamic forces. It is shown that the corresponding transport coefficients are proportional to each other, which leads to the possibility of defining a generalized thermal force and a single transport coefficient. The behavior of such conductivity with the temperature and chemical potential is analyzed and a discussion on its dependence with the relaxation parameter is also included. The relevance and applications of the results are briefly addressed.

show abstract

Heat Flux for a Relativistic Dilute Bidimensional Gas

Cited by 12 publications

References 24 publications

Dissipative properties of relativistic two-dimensional gases

Dissipative properties of relativistic two-dimensional gases

Relativistic dissipation obeys Chapman-Enskog asymptotics: Analytical and numerical evidence as a basis for accurate kinetic simulations

Thermal Dissipation in Two Dimensional Relativistic Fermi Gases with a Relaxation Time Model

Contact Info

Product

Resources

About