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Mass flow rate measurement of thermal creep flow from transitional to slip flow regime

Published online by Cambridge University Press:  20 April 2016

Hiroki Yamaguchi ,
Pierre Perrier ,
Minh Tuan Ho ,
J. Gilbert Méolans ,
Tomohide Niimi  and
Irina Graur
Hiroki Yamaguchi*
Affiliation:
Department of Micro-Nano Systems Engineering, Nagoya University, Furo-cho, Chikusa, Nagoya, Aichi 464-8603, Japan
Pierre Perrier
Affiliation:
Aix-Marseille Université, CNRS, IUSTI UMR 7343, 5 rue Enrico Fermi, 13453 Marseille, France
Minh Tuan Ho
Affiliation:
Aix-Marseille Université, CNRS, IUSTI UMR 7343, 5 rue Enrico Fermi, 13453 Marseille, France James Weir Fluids Laboratory, Department of Mechanical and Aerospace Engineering, University of Strathclyde, James Weir Building, 75 Montrose Street, Glasgow G1 1XJ, UK
J. Gilbert Méolans
Affiliation:
Aix-Marseille Université, CNRS, IUSTI UMR 7343, 5 rue Enrico Fermi, 13453 Marseille, France
Tomohide Niimi
Affiliation:
Department of Micro-Nano Systems Engineering, Nagoya University, Furo-cho, Chikusa, Nagoya, Aichi 464-8603, Japan
Irina Graur
Affiliation:
Aix-Marseille Université, CNRS, IUSTI UMR 7343, 5 rue Enrico Fermi, 13453 Marseille, France
*
†Email address for correspondence: hiroki@nagoya-u.jp
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Abstract

Measurements of the thermal creep flow through a single rectangular microchannel connected to two tanks maintained initially at the same pressure, but at different temperatures, are carried out for five noble gas species, over a large range of pressure and for two temperature differences between the tanks. The time-dependent pressure variations in both cold and hot tanks are investigated, and the temperature-driven (thermal creep) mass flow rate between two tanks is calculated from these data for the rarefaction parameter ranging from the transitional to slip flow regime. The measured mass flow rate is compared with the numerical solution of the S-model kinetic equation, and they show good agreement. A novel approximate expression to calculate the temperature-driven mass flow rate in the transitional and slip flow regimes is proposed. This expression provides results in good agreement with the measured values of the mass flow rate. In the slip flow regime, the thermal slip coefficient is calculated by employing the previously reported methodology, and the influence of the nature of the gas on this coefficient is investigated. The measured values of the thermal slip coefficient agree well with the values available in the literature, indicating that this coefficient is independent of the shape of a channel.

JFM classification

Micro-/Nano-fluid dynamics: Micro-/Nano-fluid dynamics Micro-/Nano-fluid dynamics: Non-continuum effects Rarefied Gas Flow: Rarefied Gas Flow

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Type
Papers
Information
Journal of Fluid Mechanics , Volume 795 , 25 May 2016 , pp. 690 - 707
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© 2016 Cambridge University Press 

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