On the validity of Fourier's law in systems with spatially varying strain rates

Non-equilibrium molecular dynamics (NEMD) simulations are used to study the generation of heat fluxes in systems with spatially varying shear rates. We show that the kinetic temperature, when used in Fourier's law of heat conduction, does not correctly account for the heat flux, and that the normal temperature as described by Rugh (1997, Phys. Rev. Lett., 78, 772), should be used. Only in the absence of normal temperature gradients can heat fluxes due to strain rate coupling be correctly calculated.