Effective thermal conductivity of rectangular nanowires based on phonon hydrodynamics

TL;DR

This paper develops a mathematical model based on phonon hydrodynamics to analyze the effective thermal conductivity of rectangular nanowires, revealing how shape and boundary conditions influence heat transport at the nanoscale.

Contribution

It introduces a new model using the Guyer--Krumhansl equation with slip boundary conditions to predict thermal conductivity in nanowires of various shapes and compares results with experimental data.

Findings

Square nanowires are less efficient than circular ones in thermal transport.

Circular nanowires outperform square nanowires due to absence of corners.

The model accurately fits experimental data for Si nanowires at room temperature.

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.