# Measuring Heat Flux Beyond Fourier's law

## TL;DR

This study uses nonequilibrium molecular dynamics to analyze how shear flow influences heat flux, revealing additional shear-dependent components and validating theoretical predictions about heat transfer beyond Fourier's law.

## Contribution

The paper introduces a detailed molecular dynamics approach to quantify shear-induced heat flux components, extending Fourier's law to include shear effects in thermal conductivity.

## Key findings

- Heat flux in flow direction varies linearly with strain rate.
- Additional shear-dependent heat flux components are quantified.
- Results are consistent with theoretical predictions and experimentally testable.

## Abstract

We use nonequilibrium molecular dynamics (NEMD) to explore the effect of shear flow on heat flux. By simulating a simple fluid in a channel bounded by tethered atoms, the heat flux is computed for two systems: a temperature driven one with no flow and a wall driven, Couette flow system. The results for the temperature driven system give the Fourier's law thermal conductivity, which is shown to agree well with experiments. Through comparison of the two systems, we quantify the additional components of the heat flux parallel and normal to the walls due to shear flow. To compute the heat flux in the flow direction, the Irving-Kirkwood equations are integrated over a volume, giving the so-called volume average form, and they are also manipulated to get expressions for the surface averaged and method of planes forms. The method of planes and volume average forms are shown to give equivalent results for the heat flux when using small volumes. The heat flux in the flow direction is obtained consistently over a range of simulations, and it is shown to vary linearly with strain rate, as predicted by theory. The additional strain rate dependent component of the heat flux normal to the wall is obtained by fitting the strain rate dependence of the heat flux to the expected form. As a result, the additional terms in the thermal conductivity tensor quantified in this work should be experimentally testable.