Continuum Mechanics and Thermodynamics

, Volume 24, Issue 4–6, pp 339–346 | Cite as

Quantum size effects on classical thermosize effects

Original Article


Thermosize effects have been proposed in literature by considering the quantum size effects (QSE) induced by the wave character of particles. These effects appear only if nano and macro domains are connected to each other when they are under a temperature gradient. QSE are noticeable in nano domain while they are almost negligible in macro domain. This difference causes thermosize effects, which may be called quantum thermosize effects (QTSE) because of their pure quantum origin. On the other hand, also classical thermosize effects (CTSE) appear as a result of different transport regimes in nano and macro domains, and they can be noticeable even if QTSE are negligible. As long as the mean free path (l) is much greater than the mean de Broglie wave length of particles (λ), which is almost the case in practice λ/l < 1, the principal effects are CTSE. QSE cause only small corrections on CTSE when the scale is down to nanoscale. On the other hand, in literature, QTSE and CTSE have been examined individually although it is not possible to observe QTSE alone in practice except for the extreme case of \({\lambda /l \gg 1}\) . Furthermore, the constant pressure assumption and the Knudsen law have been used during the derivations of QTSE and CTSE, respectively, although the proper assumption at nanoscale is the modified Knudsen law, which considers QSE. In this study, QSE on CTSE are considered and the modified Knudsen law is derived and used to obtain the more realistic results for thermosize coefficients. The results can be used for a possible experimental verification of thermosize effects as well as to design some new devices based on these effects.


Thermosize effects Quantum size effects Nano thermodynamics Knudsen law 


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Energy InstituteIstanbul Technical UniversityMaslak, IstanbulTurkey

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