Asymptotic Solutions of Pressure and Heat Flux of Highly Rarefied Gas Flows in Vacuum Packaged Micro-Electro-Mechanical System Devices

(*) Corresponding author

Authors' affiliations

DOI's assignment:
the author of the article can submit here a request for assignment of a DOI number to this resource!
Cost of the service: euros 10,00 (for a DOI)


This study analyzed a highly rarefied gas flow fields inside an enclosure. The enclosure is formed by four plates with two different temperatures. The plate surfaces are assumed completely diffuse; at the final steady flow stage for any point inside the enclosure or at the surface, the velocity distribution function was determined and all the macroscopic properties was determined by integrating the velocity distribution function.
First, the collisionless flow solution was considered as the base solution, and then based on the Bhatnagar-Gross-Krook model, the characteristic relaxation time scale τ was used as a small parameter, and obtained general asymptotic analytical solutions for the flow fields and heat transfer expressions. To validate these asymptotic solutions, a series of numerical simulations with the direct simulation Monte Carlo method were performed and compared with the analytical results.
In general, as Knudsen number decreases, the solutions for the pressure, temperature, and density fields deteriorate; the temperature fields had relatively better agreement than the density and pressure fields.

Copyright © 2013 Praise Worthy Prize - All rights reserved.


Heat Transfer; Rarefied Flows; Micro-Electro-Mechanical System Devices; Monte Carlo Simulation Method

Full Text:



C. Ho and Y. Tai, Micro-Electro-Mechanical-Systems (MEMS) and Fluid Flows. Annu. Rev. of Fluid Mech. Vol. 30, pp. 579, 1998.

S. Lyshevski, MEMS and NEMS: Systems, Devices, and Structures (CRC Press, 2002).

C. Cai, I. D. Boyd, J. Fan, and G. V. Candler, Direct Simulation Methods For Low-Speed Microchannel Flows. J. Thermophy. Heat Tranfser, Vol. 14, pp.368 ,2000.

H. Liu, M. Wang, J. Wang, G. Zhang, H. Liao, R. Huang, and X. Zhang, Monte Carlo Simulations of Gas Flow and Heat Transfer in Vacuum Packaged MEMS Devices. Appl. Therm. Engineering, Vol. 27, pp.323, 2007.

H. Yang, M. Wu, and W. Fang, Localized induction heating solder bonding for wafer level. MEMS packaging, J. Micromech. Microeng. Vol. 15, pp. 394, 2005.

C. Cai, Heat Transfer in vacuum packaged micro-electro-mechanical system devices. Physics of Fluids, Vol. 20, 2008.

K. Aoki, S. Takata, and H. Aikawa, A rarefied gas flow caused by a discontinuous wall temperature. Physics of Fluids, Vol. 13, pp. 2645, 2001.

G. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows. (2nd ed, Claredon Press, 1994).

C. Cai and D. Danny, Collisionless gas flows .I. Inside arbitrary enclosure. Physics of Fluids, Vol. 20, pp. 1, 2008.

M. Wang and Z. Li, Simulations for gas flows in microgeometries using the direct simulation Monte Carlo method. Int. J. Heat and Fluid Flow, Vol. 25, pp. 975-985, 2004.

I. Boyd, G. Chen, and G. Candler, Predicting failure of the continuum fluid equations in transitional hypersonic flows. Physics of Fluids, Vol 7, pp .210-219, 1995.

Soloot, A.H., Gholami, A., Niayesh, K., Study on post arc current and transient recovery voltage in vacuum circuit breaker, (2011) International Review on Modelling and Simulations (IREMOS), 4 (2), pp. 699-709.


  • There are currently no refbacks.

Please send any question about this web site to
Copyright © 2005-2024 Praise Worthy Prize