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Article information
2017 , Volume 22, Special issue, p.13-26
Germider O.V., Popov V.N.
Mathematical modelling of heat transfer process in a rectangular channel in the problem on the Poiseuille flow with diffuse-specular boundary conditions
The process of heat transfer in a channel of rectangular cross section in the case of mirror-diffuse reflection of gas molecules from the walls of the channel model is considered. As the basic equation describing the kinetics of the process, the equation of Williams is used. It is assumed that in the channel a constant pressure gradient is maintained. The pressure gradient is assumed small in magnitude and direction along the axis of symmetry of the channel. In this case, the deviation of the state of a rarefied gas from the equilibrium state is small. This circumstance made it possible to construct a solution of the Williams kinetic equation in the linearized form. The linearization is carried out with respect to locally equilibrium distribution function with parameters set on the channel walls. From the statistical sense of the distribution function of molecules of a gas on coordinates and velocity components the expression for the heat flux vector, depending on the accommodation coefficient of tangential momentum of gas molecules from the walls of the channel is obtained. The results obtained in this work show, that the greatest deviation of the values of heat flux obtained for a partial accommodation of gas molecules on the walls from the corresponding values, obtained for a diffuse reflection model, is observed approaching the free molecular regime. Moreover, for other flow regimes the heat flow values also increase with a decrease in the coefficient of accommodation of the tangential momentum, but more slowly, reaching an asymptotic limit in hydrodynamic flow regime. For different values of the coefficient of accommodation of the tangential momentum and the relations section sides the heat flux vector profile of the channel is built. A comparison with similar results in complete accommodation of the molecules at the channel walls is done. It is shown that for the channels with the same reduction ratio of sectional sizes of the accommodation coefficient of tangential momentum profile increases the heat flux vector in general. It is shown that for the channels with the same reduction ratio of sectional sizes the decrease of the accommodation coefficient of tangential momentum leads to an increase of heat flux profile vectors in general. The present analysis and the results can be used for comparison with empirical data in the development and optimization of microelectronic systems and nanotechnology. Considered method of constructing solutions of Williams’s model equation can also be applied to the channels of the other sectional configuration.
[full text]
Keywords: diffuse-specular reflection model, a rarefied gas, accommodation coefficient of tangential momentum
Author(s):
Germider Oksana Vladimirovna
Position: Senior Fellow
Office: Northern Arctic Federal University named after M.V. Lomonosov
Address: 163002, Russia, Arhangelsk, Str. Embankment of the Northern Dvina, 17
Phone Office: (8182) 21-61-35
E-mail: o.germider@narfu.ru
SPIN-code: 5562-3938Popov V.N.
Position: Assistent
Address: 634021, Russia, Tomsk, Str. Embankment of the Northern Dvina, 17
E-mail: vnp@tpu.ru
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Bibliography link:
Germider O.V., Popov V.N. Mathematical modelling of heat transfer process in a rectangular channel in the problem on the Poiseuille flow with diffuse-specular boundary conditions // Computational technologies. 2017. V. 22. XVII All-Russian Conference of Young Scientists on Mathematical Modeling and Information Technology. P. 13-26
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