A microbearing gas flow with different walls´ temperatures

Abstract

An analytical solution for the non-isothermal 2-D 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 oflO'^-W', which corresponds to the slip fiow. 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 infiuence of rarefaction effect. The analytical solutions of the pressure, velocity, and temperature for moderately high Reynolds numbers are presented here. For these fiow conditions the inertia, convection, dissipation, and rate at which work is done in compressing the element of fluid are presented in the second approximation, also.

The physical aspects of gas dynamic and thermal physics processes mathematical modelling of descent spacecraft’s

“…To solve the first problem, 3-D viscous gas equations were integrated [5][6][7][8][9][10]. The second problem was solved by integrating the 3-D equations of motion and heat exchange of particles [11][12][13].…”

Navier-Stokes-Fourier analytic solutions for non-isothermal Couette slip gas flow

“…Putting the solution for velocity (17) and temperature (12) into the velocity (5) and temperature (6) boundary conditions is: The constants C 1 , C 2 , C 3 , and C 4 are simply found from the system (18)-(21) numerically (the authors used a package MATHEMATICA), using the solutions for velocity (17) and temperature (12) at both walls (y = ±0.5). In the case of continuum, appropriate constants C c1 , C c2 , C c3 , and C c4 can be found by putting in the system (18)-(21) the appropriate boundary conditions at the walls:…”

“…3 the influence of temperature on the transport properties e. g. on the temperature (12) and velocity (17) profiles is presented taking into account the three values of the viscosity-temperature index a = 0 (constant dynamic viscosity and thermal conductivity), a = 0.5 (the elastic sphere molecule model) and a = 1 (Maxwellian molecules). The presented analytical solutions for the temperature (12) and velocity (17) are compared with numerical solutions of NSF system of equations for this Couette slip gas flow explained in [14] and with the appropriate DSMC solutions from [11] and [12] whereas the upper wall is warmer and moving to the right with the same velocity. The all considered conditions are the same to the ones provided by [11].…”

“…Couette flow with isothermal walls is solved analytically by regularized 13-moment equations in [5]. The analytical solutions by perturbation method were derived for micro-Couette non-isothermal [14] as well as microchannel [15] and microbearing isothermal [16] and non-isothermal [17] gas flows. Besides the perturbation method, the exact analytical solutions for micro-Couette gas flow with isothermal walls were also derived [14].…”

An analysis of the different parameters influence on the microbearing load carrying capacity

“…Two-dimensional non-isothermal compressible gas flow in microbearing with different temperatures of the walls is considered [2]. Small parameter is defined as the ratio between exit microbearing height and microbearing length: ε =h e /l.…”