Variational derivation of thermal slip coefficients on the basis of the Boltzmann equation for hard-sphere molecules and Cercignani-Lampis boundary conditions: Comparison with experimental results
| Autor: | Irina Graur, Silvia Lorenzani, Nhu Ngoc Nguyen, Pierre Perrier |
|---|---|
| Přispěvatelé: | Politecnico di Milano [Milan] (POLIMI), Aix Marseille Université (AMU), Institut universitaire des systèmes thermiques industriels (IUSTI), Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU), European Project: 643095,H2020,H2020-MSCA-ITN-2014,MIGRATE(2015), Aix Marseille Université (AMU)-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Fluid Flow and Transfer Processes
Physics [PHYS]Physics [physics] Mechanical Engineering Mass flow Mathematical analysis Computational Mechanics chemistry.chemical_element 02 engineering and technology Slip (materials science) 021001 nanoscience & nanotechnology Condensed Matter Physics 01 natural sciences Boltzmann equation 010305 fluids & plasmas Volumetric flow rate Neon Variational method chemistry Mechanics of Materials 0103 physical sciences Boundary value problem 0210 nano-technology Helium |
| Zdroj: | Physics of Fluids Physics of Fluids, American Institute of Physics, 2020, 32, pp.102011. ⟨10.1063/5.0025282⟩ Physics of Fluids, 2020, 32, pp.102011. ⟨10.1063/5.0025282⟩ |
| ISSN: | 1070-6631 1089-7666 |
| DOI: | 10.1063/5.0025282⟩ |
| Popis: | International audience; In the present paper, a variational method is applied to solve the Boltzmann equation based on the true linearized collision operator for hard-sphere molecules and the Cercignani–Lampis boundary conditions. This technique allows us to obtain an explicit relation between the first- and second-order thermal slip coefficients and the tangential momentum and normal energy accommodation coefficients, defined in the frame of the Cercignani–Lampis scattering kernel. Comparing the theoretical results with the experimental data from the work of Yamaguchi et al. [“Mass flow rate measurement of thermal creep flow from transitional to slip flow regime,” J. Fluid Mech. 795, 690 (2016)], a pair of accommodation coefficients has been extracted for each noble gas considered in the experiments. Then, these values have been used to compute, by means of our variational technique, the temperature-driven mass flow rates, and the outputs have been compared with the measurements for helium, neon, and argon. Good agreement has been obtained between the theoretical and the experimental data, within the range of validity of the proposed second-order slip model. For all the gases analyzed, the tangential accommodation coefficient is found to be much larger than the normal energy coefficient. The general trend, according to which, by increasing the molecular weight of the different gases, the values of both accommodation coefficients also increase, is confirmed in this study. |
| Databáze: | OpenAIRE |
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