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Computation of the Heat Flux in a Cylindrical Duct Within the Framework of the Kinetic Approach

  • KINETIC THEORY OF TRANSFER PROCESSES
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Journal of Engineering Physics and Thermophysics Aims and scope

Within the framework of the kinetic approach, the authors have solved the problem on rarefied-gas flow in a cylindrical duct in the presence of the longitudinal temperature gradient. The Williams kinetic equation was used as the basic equation, and the diffuse-reflection model, as the boundary condition on the duct wall. This enabled the authors to consider the solution of the problem in linearized form. To find a linear correction to the locally equilibrium distribution function, the problem was reduced to solution of a linear homogeneous partial differential equation of first order. A solution to the latter was constructed with the method of characteristics. With account taken of the obtained solution and on the basis of the statistical meaning of the distribution function of gas molecules by coordinates and velocities, the authors constructed the profile of the heat-flux vector in the duct and computed the heat flux through the duct cross section. A numerical analysis of final expressions was made. A comparison with analogous results obtained with the discrete-ordinates method has shown that the solution procedure proposed in the work leads to correct results in a wide range of values of the duct radius.

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Authors and Affiliations

  1. M. V. Lomonosov Northern (Arctic) Federal University, 17 Naberezhnaya Severnoi Dviny, Arkhangel′sk, 163002, Russia

    O. V. Germider, V. N. Popov & A. A. Yushkanov

Authors
  1. O. V. Germider
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  2. V. N. Popov
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  3. A. A. Yushkanov
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Correspondence to O. V. Germider.

Additional information

Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 89, No. 5, pp. 1352–1357, September–October, 2016.

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Germider, O.V., Popov, V.N. & Yushkanov, A.A. Computation of the Heat Flux in a Cylindrical Duct Within the Framework of the Kinetic Approach. J Eng Phys Thermophy 89, 1338–1343 (2016). https://doi.org/10.1007/s10891-016-1497-2

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  • DOI: https://doi.org/10.1007/s10891-016-1497-2

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