Non-isothermal rarefied gas flow in microtube with constant wall temperature

Abstract

In this paper, pressure-driven gas flow through a microtube with constant wall temperature is considered. The ratio of the molecular mean free path and the diameter of the microtube cannot be negligible. Therefore, the gas rarefaction is taken into account. A solution is obtained for subsonic as well as slip and continuum gas flow. Velocity, pressure, and temperature fields are analytically attained by macroscopic approach, using continuity, Navier-Stokes, and energy equations, with the first order boundary conditions for velocity and temperature. Characteristic variables are expressed in the form of perturbation series. The first approximation stands for solution to the continuum flow. The second one reveals the effects of gas rarefaction, inertia, and dissipation. Solutions for compressible and incompressible gas flow are presented and compared with the available results from the literature. A good matching has been achieved. This enables using proposed method for solving other microtube gas flows, which are common in various fields of engineering, biomedicine, pharmacy, etc. The main contribution of this paper is the integral treatment of several important effects such as rarefaction, compressibility, temperature field variability, inertia, and viscous dissipation in the presented solutions. Since the solutions are analytical, they are useful and easily applicable.

Influence of transport coefficients’ dependence on temperature for gas flow in microbearing

“…The perturbation model, used in this paper, was verified in our previous work [16][17][18][19] for: isothermal microbearing gas flow, 16 non-isothermal gas flow with equal temperatures of the walls, 17,18 and non-isothermal microbearing gas flow with different temperatures of the walls obtained for constant viscosity and thermal conductivity. 19 In this paper, a non-isothermal microbearing slip gas flow is analyzed by including the dependence of transport coefficients on the temperature.…”

“…The solution procedure is to expand the pressure, velocity, and temperature into a regular perturbation series [16][17][18][19] :…”

“…Our coefficient g, which occurs naturally in the dimensionless momentum equation ( 16) and energy equation (18), represents the bearing number L, as from equations ( 12) and ( 24) it follows that g = L/6. Besides, the bearing number L can be expressed in terms of the reference Mach number, Reynolds number, and the small parameter e as L = 6kMa 2 r Re r e .…”

Special Collection on advanced practices in aerospace and energy engineering

“…For instance, incompressible and compressible flow through microtubes, that also takes into account gas rarefication, applicable in bioengineering and MEMS (that is being increasingly employed), is investigated analytically in Guranov et al 1 and Milićev and Stevanović. 2 The presented results (pressure, velocity, and temperature profiles) match well with other results from literature and are easily applicable.…”