RESEARCH ARTICLE Copyright © 2011 American Scientific Publishers All rights reserved Printed in the United States of America Journal of Computational and Theoretical Nanoscience Vol. 8, 1–4, 2011 Classical Thermosize Effects in Degenerate Quantum Gases Gulru Babac and Altug Sisman ∗ Energy Institute, Istanbul Technical University, Istanbul, Turkey Classical thermosize effects arise due to different transport characteristics of macro and nano parts of a macro/nano combined system. In this paper, classical thermosize effects are considered for Fermi and Bose gases. The Knudsen law is generalized for ideal gases including the quantum ones and some analytical expressions for thermosize effects are obtained for degenerate Fermi and Bose gases. The influence of the quantum degeneracy on the classical thermosize effects are analyzed and the comparison with the results of the Maxwellian case is given. It is seen that degeneration improves the classical thermosize effects for a Bose gas while it deteriorates the effects for a Fermi gas. Keywords: Classical Thermosize Effects, Knudsen Law, Quantum Gases. 1. INTRODUCTION Gas transport in nano systems has attracted a great deal of attention recent years. 1–5 In micro/nano systems, the mean free path of the particles is comparable with the characteristic size of the domain and the flow characteris- tics of gases can considerably change from macro to nano by depending on the domain size. The flow characteris- tic in a system is determined by Knudsen number (l/L), which is the ratio of mean free path of particles (l) to the characteristic length (L) of the domain. According to mag- nitude of the Knudsen number, flow regime is generally classified as continuum (or hydrodynamic) Kn < 10 -3 , slip flow 10 -3 < Kn < 10 -1 , transition 10 -1 < Kn < 10 and free molecular flow Kn > 10. 1 Because of the size dependence of flow characteristic, gas flows in macro and nano domains are not the same and change by depending on the domain sizes. Therefore, different flow character- istics appear in macro and nano systems even if they are under the same temperature gradient. This introduce some new effects and phenomena such as Knudsen process, 6–9 thermal creeping, 10–12 quantum thermosize effects 13–15 and classical thermosize effects, 16 which cannot be observed at the macro scale. The classical thermosize effects (CTSE) arises due to changes of flow characteristics of gases from macro to nano and vice versa. CTSE has been analyzed for Maxwellian gases in the literature by considering a rect- angular box divided in macro and nano parts. 16 When a ∗ Author to whom correspondence should be addressed. temperature gradient applies to the box, the different trans- port processes are performed in each side and the flow characteristics are determined as hydrodynamic and free molecular flow in macro and nano parts respectively. The different flow characteristics also correspond to different thermodynamic processes which are defined as constant pressure process in macro part and Knudsen process (pres- sure over square root of temperature is constant) in nano part. In this paper, the classical thermosize effects are exam- ined for Fermi and Bose gases and the results are com- pared with those of Maxwell gas given in Ref. [16]. The influence of the quantum degeneracy on the CTSE is examined and discussed. 2. THERMOSIZE EFFECTS FOR QUANTUM GASES AND THE GENERALIZED KNUDSEN LAW To examine the CTSE for quantum gases, a rectangular box is considered as the same geometrical configuration chosen in Ref. [16]. The box is separated in macro and nano parts and thermally in contact with high (T H ) and low (T L ) temperature reservoirs, Figure 1. At low temperature side, there is no separator and gas flow is allowed between point 2 and point 3, whereas it is not the case at high temperature side. In steady state, local thermodynamic equilibrium conditions are provided between the points 2 and 3. In nano part of the system, the characteristic flow length is much smaller than the mean free path of particles J. Comput. Theor. Nanosci. 2011, Vol. 8, No. 11 1546-1955/2011/8/001/004 doi:10.1166/jctn.2011.1964 1