Experimental demonstration of a generalized Fourier's Law for non-diffusive thermal transport

Abstract

Phonon heat conduction over length scales comparable to their mean free paths is a topic of considerable interest for basic science and thermal management technologies. Although the failure of Fourier's law beyond the diffusive regime is well understood, debate exists over the proper physical description of thermal transport in the ballistic to diffusive crossover. Here, we derive a generalized Fourier's law that links the heat flux and temperature fields, valid from ballistic to diffusive regimes and for general geometries, using the Peierls-Boltzmann transport equation within the relaxation time approximation. This generalized Fourier's law predicts that thermal conductivity not only becomes nonlocal at length scales smaller than phonon mean free paths, but also requires the inclusion of an inhomogeneous nonlocal source term that has been previously neglected. We demonstrate the validity of this generalized Fourier's law through direct comparison with time-domain thermoreflectance (TDTR) measurements in the nondiffusive regime without adjustable parameters. Furthermore, we show that interpreting experimental data without this generalized Fourier's law leads to inaccurate measurement of thermal transport properties.

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Cited by in corpus (11)

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• Thermal Conductivity of BAs under Pressure
• Strong Temperature Dependence of Thermal Conductivity in High-Purity Cubic Boron Arsenide
• Theory of Transient Heat Conduction
• Non-monotonic heat dissipation phenomenon in close-packed quasi-2D and 3D hotspot system
• Non-local thermal transport modeling using the thermal distributor
• Phonon Boltzmann equation non-local in space and time: the partial failure of the generalized Fourier law
• A novel transient heat conduction phenomenon to distinguish the hydrodynamic and (quasi) ballistic phonon transport
• Phonon Gravity, Non-equilibrium QFT, and the Tolman Thermal Equivalence Principle
• Thermal transport in crystals: from the quantum Dyson equation to mesoscopic phonon hydrodynamics