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Research Papers

Theoretical Two-Dimensional Modeling of Gas Conduction Between Finite Parallel Plates in High Vacuum

[+] Author and Article Information
Taishan Zhu, Wenjing Ye

 Hong Kong University of Science and Technology,Clear Water Bay, Kowloon, Hong Kong, Chinamewye@ust.hk

J. Heat Transfer 134(5), 051013 (Apr 13, 2012) (6 pages) doi:10.1115/1.4005704 History: Received April 26, 2010; Revised August 25, 2010; Published April 11, 2012; Online April 13, 2012

A theoretical approach based on gaskinetic theory is described and applied for the modeling of steady-state free-molecule gaseous heat conduction within a diffusive enclosure. With a representative model of microelectromechanical system (MEMS) devices with integrated heaters, the heat transfer between the heated component and its gaseous ambient enclosed in a high vacuum is studied in detail. A molecular simulation based on the direct simulation Monte Carlo (DSMC) method is also employed to validate the theoretical solutions and to study the effects of incomplete thermal accommodation. The impacts of the finite size of the heated beam as well as the gap between the beam and a substrate on the heat transfer are investigated to examine the appropriateness of the common assumptions employed in the modeling of Pirani sensors. Interesting phenomena that are unique in the free-molecule regime are observed and discussed. These studies are valuable to the design of MEMS devices with microheaters.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Left: schematic geometry of the model problem and illustration of the reachable walls of two representative points in the domain; take point P for instance, the reflected molecules that can reach to this point come from the upper beam surface and the upper chamber wall between points A and B. Right: velocity phase space of point P; the angles define the molecular velocity space of the ith wall that is reachable by P.

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Figure 2

Schematic illustration of the polar angles centered at point P of various objects. Different shapes denote different circumstances: (a) triangles denote the cases when the dashed angle is embedded in the solid angle; (b) rectangles represent the situations where the angles overlap partially; (c) circles signify the cases where two angles do not interact.

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Figure 3

Contours of temperature (a), pressure (b), heat flux (c) when Knc  = 112.55. Left halves present the comparisons between the theoretical results (solid lines) and DSMC simulations (dashed lines); right halves demonstrate the gradual changes of corresponding quantities in space. Heat flow field is also plotted in (c).

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Figure 4

Average heat fluxes at different beam and substrate temperatures; both gap height and beam width are 10 μm. The minus sign indicates that the heat is flowing out of the beam.

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Figure 5

Average heat flux versus accommodation coefficient σT; solid lines denote the average heat flux when only the thermal accommodation coefficient of the beam is varied; dashed lines represent the heat fluxes when the thermal accommodation coefficient of the substrate is varied

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Figure 6

Normalized heat flux versus gap height; beam width is 10 μm and the temperatures of the beam, substrate, and chamber are 500 K, 450 K, and 300 K, respectively. The average heat fluxes are normalized using the values corresponding to a gap of 1 μm.

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Figure 7

The relative difference between the calculated heat fluxes at different widths and the theoretical solutions based on the infinite parallel-plate assumption; the gap height is kept at 10 μm.

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Figure 8

Heat flux fields of cases with different beam widths, gap is 5 μm and the width-gap ratios are (a) 2, (b) 5, and (c) 10.

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