## THERMAL SCIENCE

International Scientific Journal

### 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

**THERMAL SCIENCE** YEAR

**2012**, VOLUME

**16**, ISSUE

**1**, PAGES [119 - 132]

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