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

We consider unsteady heat transfer in a one-dimensional harmonic crystal surrounded by a viscous environment and subjected to an external heat supply. The basic equations for the crystal particles are stated in the form of a system of stochastic differential equations. We perform a continualization...

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Bibliographic Details
Published in:Continuum mechanics and thermodynamics 2019-01, Vol.31 (1), p.255-272
Main Authors: Gavrilov, S. N., Krivtsov, A. M., Tsvetkov, D. V.
Format: Article
Language:English
Subjects:
Classical and Continuum Physics
Covariance
Crystals
Differential equations
Engineering Thermodynamics
Heat and Mass Transfer
Heat transfer
Mathematical analysis
Original Article
Partial differential equations
Physics
Physics and Astronomy
Structural Materials
Theoretical and Applied Mechanics
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Summary:We consider unsteady heat transfer in a one-dimensional harmonic crystal surrounded by a viscous environment and subjected to an external heat supply. The basic equations for the crystal particles are stated in the form of a system of stochastic differential equations. We perform a continualization procedure and derive an infinite set of linear partial differential equations for covariance variables. An exact analytic solution describing unsteady ballistic heat transfer in the crystal is obtained. It is shown that the stationary spatial profile of the kinetic temperature caused by a point source of heat supply of constant intensity is described by the Macdonald function of zero order. A comparison with the results obtained in the framework of the classical heat equation is presented. We expect that the results obtained in the paper can be verified by experiments with laser excitation of low-dimensional nanostructures.
ISSN:0935-1175
1432-0959
DOI:10.1007/s00161-018-0681-3