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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 x-direction. 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 compressing the element of fluid are also presented in the second approximation.
KEYWORDS
PAPER SUBMITTED: 2011-06-01
PAPER REVISED: 2011-08-04
PAPER ACCEPTED: 2011-08-05
DOI REFERENCE: https://doi.org/10.2298/TSCI110804086M
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2012, VOLUME 16, ISSUE 1, PAGES [119 - 132]
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© 2019 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence