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In the paper we deal with ballistic heat transport in a graphene latticesubjected to a point heat source. It is assumed that a graphene sheet issuspended under tension in a viscous gas. We use the model of a harmonicpolyatomic (more exactly diatomic) lattice performing out-of-plane motions. Thedynamics of the lattice is described by an infinite system of stochasticordinary differential equations with white noise in the right-hand side, whichmodels the point heat source. On the base of the previous analytical unsteadyanalysis an analytical formula in continuum approximation is suggested, whichallows one to describe a steady-state kinetic temperature distribution in thegraphene lattice in continuum approximation. The obtained solution is in a goodagreement with numerical results obtained for the discrete system everywhereexcepting a neighbourhood of six singular rays with the origin at the heatsource location. The continuum solution becomes singular at these rays, unlikethe discrete one, which appears to be localized in a certain sense along therays. The factors, which cause such a directional localization and the mismatchbetween the continuum and discrete solutions are discussed. We expect that thesuggested formula is applicable for various damped polyatomic lattices whereall particles have equal masses in the case of universal for all particlesexternal viscosity.

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