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Dynamical Analysis of Non-Fourier Heat Conduction and Its Application in Nanosystems

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Abstract

The traditional Fourier’s law of heat conduction is not applicable in ultrafast and ultrasmall conditions. Non-Fourier models thus have been developed to predict these anomalous heat conductions. This chapter reviews the present non-Fourier heat conduction theories. For ultrafast heat conduction, modification models such as the Cattaneo–Vernotte model, dual phase lag model, and hyperbolic two-step model are developed. The common feature of these models is adding the relaxation terms in the traditional Fourier’s law. For the steady non-Fourier heat conduction in nanosystems, the size effect of the thermal conductivity has been modeled from the phonon-boundary scattering perspective. On the other hand, the combination of non-Fourier conduction models with irreversible thermodynamics will give the negative entropy production, which violates the second law. The extended irreversible thermodynamics modifies the entropy production by extending the category of state variables to mend this paradox. At the end of this chapter, the approach and main aim of this work are presented.

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  1. Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Engineering Mechanics, Tsinghua University, Beijing, China

    Yuan Dong

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Dong, Y. (2016). Introduction. In: Dynamical Analysis of Non-Fourier Heat Conduction and Its Application in Nanosystems. Springer Theses. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48485-2_1

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