Journal of Thermal Engineering

Öz

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.