Search for the heat flow profile and gas mass velocity in a cylindrical channel

Anatoliy A. Sadkov, Vasiliy N. Popov


Problems of modeling the movement of a rarefied gas in a cylindrical channel are considered. The study is based on the Boltzmann equation, which makes it possible to study various gas parameters. The study of the Boltzmann equation with the Maxwell boundary condition makes it possible to form an algorithm of a mathematical model for the formation of detailed data on the profile of heat fluxes and the mass velocity of gas in a cylindrical channel in accordance with the properties of the environment. The basis for the choice of numerical methods for solving the problem according to a given algorithm significantly affects the accuracy of searching for detailed data, the «bottlenecks» in this algorithm are the calculation of the values of the inverse matrix and the integral, where one or another method of searching for values in grid nodes is selected to form the final resulting value or set of values. The calculation of detailed data according to the formulated algorithm was developed in the Microsoft Visual Studio 2017 software development environment, and the algorithm itself is described using the C ++ programming language. The calculations were carried out using various simulations as using a sequential set of actions, i.e. linear programming and parallel programming on a processor / video card, to identify the difference in calculations in time and accelerate the receipt of the resulting data. For the accuracy of calculating the final detailed data with an accuracy of five decimal places, the Simpson method was used to find the value of the integral, and the LU-expansion method was used to find the values of the inverse matrix.

Full Text:

PDF (Russian)


Barichello, L. B. A Discrete-Ordinates Solutions for Poiseuille Flow in a Plane Channel / L. B. Barichello, C. E. Siewert // Zeitschrift fur Angewandte Mathematic und Physik. 1999. – V. 50. – p. 972-981.

Barichello, L. B. Unified solutions to classical flow problems based on the BGK model / L. B. Barichelloet al. // Zeitschrift fur Angewandte Mathematic und Physik. 2001 – V.-52. – p. 517-534.

Siewert, C. E. Poiseuille, Thermal Creep and Couette Flow: Results Based on the CES Model Linearized Boltzmann Equation / C. E. Siewert // European Journal of Mechanics B/Fluids, 2002. – V. 21. – p. 579-597.

Siewert, C. E. Model equations in rarefied gas dynamics: viscous-slip and thermal-slip coefficients / C. E. Siewert, F. Sharipov // Phys. Fluids, 2002. – V. 14. No 12. – p. 4123-4129.

Siewert, C. E. The linearized Boltzmann Equation: Concise and Accurate Solutions to Basic Flow Problems / C. E. Siewert // Zeitschrift fur Angewandte Mathematic und Physik, 2003. – V. 54. – p. 273-303.

Germinder, О.V. An analytic solution of the poiseuille problem in a direct elliptic cylinder with a mirror-diffusive boundary condition on the walls / О.V. Germinder, V.N. Popov // Физический вестник высшей школы естественных наук и технологий САФУ. – 2017. – p. 3-11.

Germinder, О.V. Mathematical simulation of heat and mass transfer in a cylindrical channel versus the tangential momentum accommodation coefficient / О.V. Germinder, V.N. Popov // Technical physics. the russian journal of applied physics. - 2017. – T. 87. № 11. – p. 1605-1610.

Germinder, О.V. Heat and mass fluxes upon incomplete accommodation of rarefied gas molecules by the walls of an elliptic channel / О.V. Germinder, V.N. Popov //Изв. РАН. МЖГ. – 2017. – № 5. – С. 103-109.


  • There are currently no refbacks.

Abava  Absolutech Convergent 2020

ISSN: 2307-8162