Abstract
This paper presents a new formulation of the
 rate of entropy generation in thin films whose thickness is of the order of the
 mean-free-path or less. In this relation, an expression for the gradient of the
 equivalent equilibrium temperature is proposed that is a function of the
 gradient of the phonon intensity at any point inside the thin film. It is shown
 that the proposed expression reduces to the familiar gradient of the
 thermodynamic temperature in the diffusive limit. Furthermore, the new
 formulation is used to compute the entropy generation rate for the case of
 steady-state, one-dimensional heat transfer in a thin film by first solving the
 Equation of Phonon Radiative Transfer to determine the phonon intensity. These
 computations are performed both for the silicon and the diamond thin films, for
 a range of Knudsen numbers starting from the diffusive limit up until the
 ballistic limit. It is found that the entropy generation rate attains a peak
 value at Kn = 0.7 and decreases for other Knudsen numbers when non-equilibrium
 transport is adopted in the analysis. However, rate of entropy generation increases
 almost linearly for the equilibrium heating situation. This is true for both
 the silicon and the diamond thin films.
Highlights
Energy transport across the thin film films involves with non-equilibrium processes, which can be described through the wave nature of transfer characteristics
Phonons are the waves, which govern the energy transfer inside the thin films when the film is thermally disturbed from the edges
One of the key factors effecting the transport characteristics is the ratio of phonon mean free path of the film over the film size, which is described through the Knudsen number (Kn)
Summary
Energy transport across the thin film films involves with non-equilibrium processes, which can be described through the wave nature of transfer characteristics. For the condition when Kn 1, the continuum approach describing the energy transport across the film fails the describe the phenomena correctly because of the ballistic contribution of large wavelength phonons In this case, the ballistic phonons do not undergo scattering in the film, they rather jump across the film edges while not seeing the film resistance to the thermal transport. The ballistic phonons do not undergo scattering in the film, they rather jump across the film edges while not seeing the film resistance to the thermal transport Describing such transfer processes incorporating the classical approaches, such as Fourier model, fails to predict the correct temperature rise or equilibrium phonon intensity distribution in the film. Various approaches can possibly be considered to formulate the entropy generation rate within the film such as the one purposed in the present study
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