ENTROPY GENERATION RATE IN A MICROSCALE THIN FILM

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.

Keywords:

Phonon Transport, Non-equilibrium Heating, Thin Films Entropy Generation Rate,

PDF

___

[1] Majumdar, A. S. M. E. (1993). Microscale heat conduction in dielectric thin films. Journal of Heat Transfer, 115(1), 7-16.
[2] Planck, M. (1959). The Theory of Heat Radiation. Dover: New York.
[3] Caldas, M., Semiao, V. (2005). Entropy generation through radiative transfer in participating media: analysis and numerical computation. Journal of Quantitative Spectroscopy and Radiative Transfer, 96(3-4), 423-437.
[4] Liu, L. H., Chu, S. X. (2006). On the entropy generation formula of radiation heat transfer processes. Journal of heat transfer, 128(5), 504-506.
[5] Zhang, Z. M., Basu, S. (2007). Entropy flow and generation in radiative transfer between surfaces. International journal of heat and mass transfer, 50(3-4), 702-712.
[6] Bright, T. J., Zhang, Z. M. (2010). Entropy generation in thin films evaluated from phonon radiative transport. Journal of Heat Transfer, 132(10), 101301.
[7] Ali, H., Yilbas, B. S. (2014). Entropy generation in silicon thin film: Influence of film thickness on entropy generation rate. Journal of Non-Equilibrium Thermodynamics, 39(3), 147-158.
[8] Aziz, A., Khan, W. A. (2012). Entropy generation in an asymmetrically cooled slab with temperature‐dependent internal heat generation. Heat Transfer—Asian Research, 41(3), 260-271.
[9] Yilbas, B. S., Mansoor, S. B., Ali, H. (2017). Heat Transport in Micro-and Nanoscale Thin Films. Elsevier.

Başlangıç: 2015
Yayıncı: YILDIZ TEKNİK ÜNİVERSİTESİ

Arşiv