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Exact harmonic solutions to Guyer–Krumhansl-type equation and application to heat transport in thin films

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Abstract

A system of hyperbolic-type inhomogeneous differential equations (DE) is considered for non-Fourier heat transfer in thin films. Exact harmonic solutions to Guyer–Krumhansl-type heat equation and to the system of inhomogeneous DE are obtained in Cauchy- and Dirichlet-type conditions. The contribution of the ballistic-type heat transport, of the Cattaneo heat waves and of the Fourier heat diffusion is discussed and compared with each other in various conditions. The application of the study to the ballistic heat transport in thin films is performed. Rapid evolution of the ballistic quasi-temperature component in low-dimensional systems is elucidated and compared with slow evolution of its diffusive counterpart. The effect of the ballistic quasi-temperature component on the evolution of the complete quasi-temperature is explored. In this context, the influence of the Knudsen number and of Cauchy- and Dirichlet-type conditions on the evolution of the temperature distribution is explored. The comparative analysis of the obtained solutions is performed.

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Change history

  • 05 April 2018

    Unfortunately, Eq. (14) was incorrectly published in the original publication and the correct equation is provided here.

  • 05 April 2018

    Unfortunately, Eq. (14) was incorrectly published in the original publication and the correct equation is provided here.

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  1. Faculty of Physics, M.V. Lomonosov Moscow State University, Leninskie Gory, Moscow, Russia, 119991

    K. Zhukovsky & D. Oskolkov

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  1. K. Zhukovsky
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  2. D. Oskolkov
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Correspondence to K. Zhukovsky.

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Communicated by Attila R. Imre.

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Zhukovsky, K., Oskolkov, D. Exact harmonic solutions to Guyer–Krumhansl-type equation and application to heat transport in thin films. Continuum Mech. Thermodyn. 30, 1207–1222 (2018). https://doi.org/10.1007/s00161-018-0648-4

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