ISSN 2079-6900 (Print)
ISSN 2587-7496 (Online)

#### Middle Volga Mathematical Society Journal

MSC2020 76D05 80A19 35B40

### Asymptotic study of heat and mass transfer in weakly twisted jets

#### P. A. Velmisov1, U. J. Mizher2, V. N. Kovalnogov3

Annotation Jet flows of liquids and gases are used in various fields of technology as means of controlling the processes of heat and mass transfer, for the intensification and stabilization of the combustion process, as means of protecting structures from exposure to thermal fields, for coating, etc. The jets of liquids and gases in technology are formed by sources-nozzles of finite sizes with various distributions of the initial outflow velocities in the outlet section of the nozzle, therefore, the calculation of the aerodynamic and thermal characteristics of jet flows is reduced to solving non-self-similar problems. However, one of the methods for solving such problems is the method of asymptotic expansion of velocities and pressure in series in a small parameter, when the first member of this series is a self-similar solution to the jet source problem. This article proposes an asymptotic expansion for axisymmetric weakly swirling flows in a model of a viscous incompressible medium, which leads to nonlinear «boundary layer» equations that differ from the well-known classical equations [1]–[4] for flows with finite swirl. Self-similar solutions of these equations are constructed that describe the distribution of speed, pressure, and temperature in a weakly swirling jet. The results presented in the article complement the results of [3]–[7] by calculating the thermal field in the jet. aerohydrodynamics, swirling jet, viscosity, asymptotic expansion, self-similar solutions, heat and mass transfer

1Peter A. Velmisov, Head of the Department of Higher Mathematics, Ulyanovsk State Technical University (32 Severny Venets St., Ulyanovsk 432027, Russia), Professor, Doctor of Physical and Mathematical Sciences, ORCID: https://orcid.org/0000-0001-7825-7015, velmisov@ulstu.ru

2Usama J. Mizher, Postgraduate Student, Department of Higher Mathematics, Ulyanovsk State Technical University (32 Severny Venets St., Ulyanovsk 432027, Russia), Postgraduate Student, ORCID: http://orcid.org/0000-0002-8950-9772, usama.mizher@gmail.com

3Vladislav N. Kovalnogov, Head of the Department of Thermal Power Engineering, Ulyanovsk State Technical University (32 Severny Venets St., Ulyanovsk 432027, Russia), Doctor of Technical Sciences, ORCID: https://orcid.org/0000-0002-1907-3790, kvn@ulstu.ru

Citation: P. A. Velmisov, U. J. Mizher, V. N. Kovalnogov, "[Asymptotic study of heat and mass transfer in weakly twisted jets]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,22:2 (2020) 200–207 (In Russian)

DOI 10.15507/2079-6900.22.202002.200-207