Non-Fourier heat transport across 1D nano film between thermal reservoirs with different boundary resistances

Abstract

We describe the nonlocal heat transport across a thin film in contact with two thermal baths using discrete variable model. The effective thermal conductivities , the boundary temperature jumps, the steady-state heat flux, and the internal temperature gradient are calculated analytically as functions of the film size and the boundary resistances. As the system size decreases, all the parameters demonstrate the transition from diffusive (Fourier) heat conduction when the scattering occurs mainly inside the film to ballistic transport when scattering occurs at the boundaries, while inside the film there is no scattering and the temperature profile is flat. We show that when the boundary resistance increases, the temperature profile inside the film also tends to be flat, but in this case the scattering, though small, occurs inside the film. The predicted effective thermal conductivity is consistent with classical continuous theories and available experimental data. • We consider heat transport across 1D nano film. • Discrete variable model has been used. • Effective thermal conductivity is size and resistance dependent. • Transition to ballistic regime is described.