12th Joint European Thermodynamics Conference Brescia, July 1-5, 2013 INTRODUCTION Nano Scale transport has a great deal of attention in recent years because of the increasing trend of manufacturing on these scales. Many transport phenomena in macro scale have to be revised or modified since many negligible effects in macro scale can be dominant in nano scale [1-3]. Quantum size effects (QSE) are one of these effects and they arise when thermal de Broglie wavelength of particles is not negligible in comparison with the characteristic size of the system. In such a case, wave character of particles becomes important and make thermodynamic and transport properties depend on shape and size of the domain [4-16]. Quantum degeneracy is another effect, which can be important in case high density or low temperature conditions. Under those conditions, thermal de Broglie wave length of particles is large enough in comparison with the mean distance between particles. Therefore quantum degeneracy becomes important and cause considerable changes in transport behaviours. In this case, quantum statistics (Fermi or Bose) should be used in calculations. Transport processes in nano domains are generally considered within the scope of free molecular transport regime in which particle wall collisions are dominate instead of particle-particle ones. Therefore, size and surface effects can be more important in free molecular flow regime. In this paper, thermal self-diffusion in free molecular transport regime is considered and both quantum degeneracy and QSE are taken into account in the calculations. Thermal self-diffusion fluxes of monatomic ideal Fermi and Bose gases (like He3 and He4) are determined. The influences of quantum degeneracy and QSE on thermal self-diffusion rates are examined. THERMAL-SELF DIFFUSION IN QUANTUM DEGENERACY LIMIT Thermal self-diffusion coefficient built up a relation between the diffusive flux and the temperature gradient and it is written in the following form T D J th      (1) Here, D th is the thermal self-diffusion coefficient, J is the particle flux due to temperature gradient, T   . To examine quantum size effects on thermal self-diffusion, nano scale transport domain is considered. Therefore free molecular transport regime is dominant since the mean free path of particles is usually larger than the characteristic size of the domain at nano scale. For ideal Maxwellian and quantum gases (Fermi and Bose) thermal self-diffusion coefficient can be given for free molecular transport regime as [17];               2 0 2 1 2 g g g mT k nL T J D B g th    (2) In Eq. (2), n is particle density, L g is the characteristic size of the domain which can be given by V/2A where V and A are domain volume and surface area respectively, k B is the Boltzmann’s constant, T is temperature, m is the particle mass and  is the dimensionless chemical potential defined as T k B    in terms of chemical potential,  . Definitions of  , 0 g and 2 g functions are given in Refs. [13, 17] and their ratios in Eq.(2) can be obtained for an ideal quantum gases (namely Fermi Dirac-FD and Bose Einstein-BE gases) as follows QUANTUM SIZE AND DEGENERACY EFFECTS ON THERMAL SELF- DIFFUSION UNDER FREE MOLECULAR TRANSPORT REGIME Gulru Babac, Altug Sisman * and Z. Fatih Ozturk Istanbul Technical University, Energy Institute, 34469 Maslak, Istanbul, Turkey. * Corresponding author, sismanal@itu.edu.tr ABSTRACT Thermal self-diffusion coefficients of monatomic ideal Fermi and Bose gases (like He3 and He4) are analytically determined by considering quantum size effects (QSE) for free molecular flow regime. The variations of thermal diffusion coefficients for Fermi and Bose gases with chemical potential are analyzed by neglecting QSE to understand the pure effect of quantum degeneracy. The results show that quantum degeneracy causes a substantial difference especially in degeneracy limit. It is seen that quantum degeneracy reduces thermal diffusion rate for both Fermi and Bose gases. There is a limit value for diffusion rate in a completely degenerate Bose gas. Furthermore, diffusion rates for Fermi and Bose gases are different from each other for the same degeneracy level. This difference in diffusion rates can be used for isotopic separation. QSE on thermal diffusion coefficients are also investigated. QSE cause tiny deviations from macroscopic behavior of thermal self-diffusion. QSE have negative contribution on thermal self-diffusion at low degeneracy while an opposite contribution appears at high degeneracy limit. Dimensionless diffusion coefficient goes to unity for a completely degenerate Fermi gas while it goes to infinity for a Bose gas. 421