Steady-state ballistic thermal transport associated with transversal motions in a damped graphene lattice subjected to a point heat source

TL;DR

This paper develops an analytical model describing steady-state ballistic thermal transport in a damped graphene lattice with out-of-plane motions, showing good agreement with numerical results except near singular rays from the heat source.

Contribution

It introduces a continuum approximation formula for temperature distribution in a damped polyatomic lattice, accounting for directional localization effects and discrepancies with discrete models.

Findings

Analytical formula accurately predicts temperature distribution in the lattice.

Continuum solution exhibits singularities along specific rays, unlike the discrete model.

Model applicable to various damped polyatomic lattices with uniform particle masses.

Abstract

In the paper we deal with ballistic heat transport in a graphene lattice subjected to a point heat source. It is assumed that a graphene sheet is suspended under tension in a viscous gas. We use the model of a harmonic polyatomic (more exactly diatomic) lattice performing out-of-plane motions. The dynamics of the lattice is described by an infinite system of stochastic ordinary differential equations with white noise in the right-hand side, which models the point heat source. On the base of the previous analytical unsteady analysis an analytical formula in continuum approximation is suggested, which allows one to describe a steady-state kinetic temperature distribution in the graphene lattice in continuum approximation. The obtained solution is in a good agreement with numerical results obtained for the discrete system everywhere excepting a neighbourhood of six singular rays with the origin at the heat source location. The continuum solution becomes singular at these rays, unlike the discrete one, which appears to be localized in a certain sense along the rays. The factors, which cause such a directional localization and the mismatch between the continuum and discrete solutions are discussed. We expect that the suggested formula is applicable for various damped polyatomic lattices where all particles have equal masses in the case of universal for all particles external viscosity.