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We consider unsteady heat transfer in a one-dimensional harmonic crystalsurrounded by a viscous environment and subjected to an external heat supply.The basic equations for the crystal particles are stated in the form of asystem of stochastic differential equations. We perform a continualizationprocedure and derive an infinite set of linear partial differential equationsfor covariance variables. An exact analytic solution describing unsteadyballistic heat transfer in the crystal is obtained. It is shown that thestationary spatial profile of the kinetic temperature caused by a point sourceof heat supply of constant intensity is described by the Macdonald function ofzero order. A comparison with the results obtained in the framework of theclassical heat equation is presented. We expect that the results obtained inthe paper can be verified by experiments with laser excitation oflow-dimensional nanostructures.

Heat transfer in a one-dimensional harmonic crystal in a viscous environment subjected to an external heat supply