  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.
