Dynamical Analysis of Heat Conduction in Nanosystems and Its Application

Part of the Springer Theses book series (Springer Theses)


The heat conduction in nanosystems deviates from the Fourier’s law. The effective thermal conductivity depends on the system size, which is understood as a result of the phonon-boundary scattering. It is proposed in this chapter that the phonon gas (the form of thermomass in dielectric materials) exhibits the viscosity and rarefication effects in nanosystems. The viscosity effect induces the nonuniform heat flux profile at each cross section, which reflects the extra boundary resistance on heat conduction. On the other hand, in nanosystems, the boundary scattering shortens the MFPs of normal processes, which reduces the effective viscosity of phonon gas. With the modification of effective MFPs, the prediction models for the in-plane heat conduction in Si nanofilms and nanowires are developed. The numerical prediction agrees well with the experiments. For the cross-plane heat conduction, the phonon distribution function transits from the ballistic one at the boundary to the diffusive one away from the boundary. A ballistic–diffusive model is thereby established based on the phonon Boltzmann equation. This model agrees well with the molecular dynamics simulations for the cross-plane thermal conductivity (CPTC) of Si nanofilms.


Heat Flux Heat Conduction Effective Thermal Conductivity Effective Viscosity Gray Model 
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© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Key Laboratory for Thermal Science and Power Engineering of Ministry of EducationDepartment of Engineering Mechanics, Tsinghua UniversityBeijingChina

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