Effective thermal conductivity of rectangular nanowires based on phonon hydrodynamics. (November 2018) - Calvo-Schwarzwälder, M.; Hennessy, M.G.; Torres, P.; Myers, T.G.; Alvarez, F.X.
Highlights: A model for heat flow across a nanowire with rectangular cross section is developed based on phonon hydrodynamics with a slip boundary condition. Asymptotic expressions for the effective thermal conductivity of the nanowire are presented and can be readily extended to non-rectangular geometries. For a fixed cross-sectional area, circular nanowires are shown to be the most efficient transporters of thermal energy, with thin films being the worst. Theoretical predictions of the effective thermal conductivity are in excellent agreement with experimental measurements. Abstract: A mathematical model is presented for thermal transport in nanowires with rectangular cross sections. Expressions for the effective thermal conductivity of the nanowire across a range of temperatures and cross-sectional aspect ratios are obtained by solving the Guyer–Krumhansl hydrodynamic equation for the thermal flux with a slip boundary condition. Our results show that square nanowires transport thermal energy more efficiently than rectangular nanowires due to optimal separation between the boundaries. However, circular nanowires are found to be even more efficient than square nanowires due to the lack of corners in the cross section, which locally reduce the thermal flux and inhibit the conduction of heat. By using a temperature-dependent slip coefficient, we show that the model is able to accurately capture experimental data of the effective thermal conductivity obtained from Si nanowires, demonstrating that phonon hydrodynamics is a powerful framework that can be applied to nanosystems even at room temperature.