Effect of the internal degrees of freedom of the gas molecules on the heat and mass transfer in long circular capillarie
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RESEARCH PAPER
Effect of the internal degrees of freedom of the gas molecules on the heat and mass transfer in long circular capillaries Christos Tantos1 · Stylianos Varoutis1 · Christian Day1 Received: 1 August 2020 / Accepted: 23 October 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract The study of the mass and heat transfer phenomena in micro-nano devices and systems (MEMS/NEMS) very often involves polyatomic gas flows in long capillaries. In the case of polyatomic gases, the internal degrees of freedom of gas molecules may have a significant effect on the macroscopic quantities of practical interest. The scope of the present study is two-fold. First, an accurate methodology for calculating the mass and heat flow rate coefficients is proposed based on a simple kinetic model proposed by Holway. The proposed methodology is based on the available experimental data in the literature and allows overcoming the well-known limitation of the Holway model to describe all the transport coefficients simultaneously. Second, the proposed methodology is applied to investigate the rarefied polyatomic gas flows through long micro- and nanotubes under temperature and pressure differences taking into account the translational, rotational and vibrational degrees of freedom of the gas molecules on the basis of the Holway kinetic model. Results are presented for N2, CO2, CH4 and SF6 representing linear and non-linear, but always non-polar molecules in a wide range of the gas temperature. The mass flow rates of the polyatomic gases in the temperature-driven flow differ significantly from the corresponding monatomic ones, with the difference reaching a maximum of about 25% for the examined gases and temperatures varied between 300 and 1000 K. The maximum relative deviation between monatomic and polyatomic heat flow rates can reach 39%, 64%, 73% and 87% for N2, CO2, CH4 and SF6, respectively. The results are compared against the corresponding published ones based on the Rykov model highlighting the very good agreement between the two models and the accuracy of the proposed methodology for the calculation of the mass and heat flow coefficients is confirmed. Keywords Polyatomic gases · Holway model · Thermal creep · Poiseuille flow · Rotational modes · Vibrational modes
1 Introduction and motivation of this work The study of the rarefied gas flows, i.e. when the mean free path of the gas becomes comparable with the characteristic length of the gas flow, through microchannels has attracted over the years considerable attention mainly due to its practical importance in several technological fields, such as the vacuum industry (Jousten 2008; Day and Murdoch 2008), aerosol industry (Ivchenko et al. 2007), porous media (Afrasiabian et al. 2013), high altitude aerodynamics (Ivanov and Gimelshein 1998; Bird 1994) and the microelectronic mechanical systems (MEMS) industry (Cercignani * Christos Tantos [email protected] 1
Institute for Technical Physics, Karlsruhe Institute of Technology, Hermann‑vo
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