A MICROBEARING GAS FLOW WITH DIFFERENT WALLS´ TEMPERATURES

Abstract

An analytical solution for the non-isothermal two-dimensional compressible gas flow in a slider microbearing with different temperatures of walls is presented in this paper. The slip flow is defined by the continuity, Navier- Stokes and energy continuum equations, along with the velocity slip and the temperature jump first order boundary conditions. Knudsen number is in the range of 10-3-10-1, which corresponds to the slip flow. The ratio between the exit microbearing height and the microbearing length is taken to be a small parameter. Moreover, it is assumed that the microbearing cross section varies slowly, which implies that all physical quantities vary slowly in xdirection. The model solution is treated by developing a perturbation scheme. The first approximation corresponds to the continuum flow conditions, while the second one involves the influence of rarefaction effect. The analytical solutions of the pressure, velocity and temperature for moderately high Reynolds numbers are presented here. For these flow conditions the inertia, convection, dissipation and rate at which work is done in ompressing the element of fluid are also presented in the second approximation.

Dates

  • Submission Date2011-06-01
  • Revision Date2011-08-04
  • Acceptance Date2011-08-05

DOI Reference

10.2298/TSCI110804086M

References

  1. Gad-El-Hak, M., The MEMS Handbook, CRC Press, 2002
  2. Burgdorfer, A., "The influence of the molecular mean free path on the performance of hydrodynamic gas lubricated bearing," J. Basic Eng. Trans, 81 (1959), pp. 94-100
  3. Mitsuya, Y., "Modified Reynolds equation for ultra-thin film gas lubrication using 1.5-order slip-flow model and considering surface accommodation coefficient," ASME J. Tribology, 115 (1993), pp. 289-294
  4. Hsia, Y., Domoto, G., "An experimental investigation of molecular rarefaction effects in gas-lubricated bearings at ultra low clearances," J. Lubr. Technol, 105 (1983), pp. 120-130
  5. Sun,Y.H., Chan, W.K., Liu, N.Y., "A slip model for gas lubrication based on an effective viscosity concept," J. Eng Tribol, 217 (2003), pp. 187-195
  6. Bahukudumbi, P., Beskok, A., "A phenomenological lubrication model for the entire Knudsen regime," J. Micromech and Microeng, 13 (2003), pp. 873-884
  7. Fukui, S., Kaneko, R., "Analysis of ultra-thin gas film lubrication based on linearized Boltzmann equation: First report-derivation of a generalized lubrication equation including thermal creep flow," J. Tribol, 110 (1988), pp. 253-262
  8. Fukui, S., Kaneko, R, "A database for interpolation of Poiseuille flow rates for high Knudsen number lubrication problems," J. Tribol, 112 (1990), pp. 78-83
  9. Liu, N., Ng, E.Y.K., "The posture effects of a slider air bearing on its performance with a direct simulation Monte Carlo method," J. Micromech. Microeng, 11 (2001), pp. 463-473
  10. Stevanovic, N., "A new analytical solution of microchannel gas flow," J. Micromech. Microeng, 17 (2007), pp. 1695-1702
  11. Stevanovic, N., "Analytical solution of gas lubricated slider microbearing," Microfluid. Nanofluid, 7 (2009), 1, pp. 97-105
  12. Stevanovic, N., Milicev, S., "A constant wall temperature microbearing gas flow," FME Transactions, 38 (2010), 2, pp. 65-71
Volume 16, Issue 1, Pages119 -132