# Article 7220

 Title of the article ASYMPTOTIC STUDY OF HEAT AND MASS TRANSFER PROCESSES IN JET FLOWS Authors Vel'misov Petr Aleksandrovich, Doctor of physical and mathematical sciences, professor, head of sub-department of higher mathematics, Ulyanovsk State Technical University (32 Severny Venets street, Ulyanovsk, Russia), E-mail: velmisov@ulstu.ru Mizher Usama Jawad, Postgraduate student, Ulyanovsk State Technical University (32 Severny Venets street, Ulyanovsk, Russia),E-mail: usama.mizher@gmail.com Tamarova Yuliya Aleksandrovna, Applicant, sub-department of higher mathematics, Ulyanovsk State Technical University (32 Severny Venets street, Ulyanovsk, Russia), E-mail: kazakovaua@mail.ru Index UDK 532.5:536.4:517.9 DOI 10.21685/2072-3040-2020-2-7 Abstract Background. Jet streams of liquids and gases are used in various fields of technology as effective means of controlling the processes of heat and mass transfer, for intensifying and stabilizing various technological processes (for example, the stirring process, the combustion process), as a means of protecting various structures from the effects of thermal and other fields, for applying coatings, etc. Among the practically important objects of research, we also note burners, engine nozzles, jetvortex traces of aircraft. Jet streams are used in many branches of engineering and technology, which makes the problem of their study urgent. The aim of this work is to study the processes of heat and mass transfer in swirling jets. Materials and methods. To solve the problem, the asymptotic method is used, which involves the expansion of hydrodynamic functions (components of the velocity vector and pressure) and temperature, satisfying the system of Navier-Stokes equations for a viscous incompressible fluid, in series with respect to a small parameter. The solution of the obtained in the first approximation system of partial differential equations is sought in a self-similar form, which leads to the study of a system of ordinary differential equations for functions depending on the selfsimilar variable. Results. In a first approximation, the self-similar solution to the problem of the distribution of hydrodynamic (components of the velocity and pressure vector) and thermal (temperature) fields in an axisymmetric tangentially swirling stream of a viscous incompressible fluid is constructed. The material presented in the article supplements the previously known results by calculating the thermal field in the jet. Conclusions. Based on the obtained asymptotic differential equations and selfsimilar solutions of these equations, the fields of velocities, pressure and temperature are constructed in a tangentially swirling stream of a viscous incompressible fluid. It is shown that the longitudinal and tangential (rotational) velocity components influence the distribution of the thermal field in the jet as a first approximation. The method for clarifying the constructed solution is indicated. Key words aerohydrodynamics, swirling jet, viscosity, heat and mass transfer, differential equations, asymptotic expansion, self-similar solution References 1. Loytsyanskiy L. G. Mekhanika zhidkosti i gaza [Fluid and gas mechanics]. Moscow: Nauka, Glavnaya redaktsiya fiziko-matematicheskoy literatury, 1978, 736 p. [In Russian] 2. Shlikhting G. Teoriya pogranichnogo sloya [Boundary layer theory]. Moscow: Nauka, Glavnaya redaktsiya fiziko-matematicheskoy literatury, 1969, 744 p. [In Russian] 3. Van-Dayk M. Metody vozmushcheniy v mekhanike zhidkosti [Perturbation methods in fluid mechanics]. Moscow: Mir, 1967, 296 p. [In Russian] 4. Koul Dzh. Metody vozmushcheniy v prikladnoy matematike [Perturbation methods in applied mathematics]. Moscow: Mir, 1972, 275 p. [In Russian] 5. Nayfe A. Metody vozmushcheniy [Perturbation methods]. Moscow, 1967. [In Russian] 6. Loytsyanskiy L. G. Prikladnaya matematika i mekhanika [Applied mathematics and mechanics]. 1953, vol. 27, no. 1, pp. 3–16. [In Russian] 7. Fal'kovich S. V. Prikladnaya matematika i mekhanika [Applied mathematics and mechanics]. 1967, vol. 31, no. 2, pp. 282–288. [In Russian] 8. Korobko V. I. Teoriya neavtomodel'nykh struy vyazkoy zhidkosti [Theory of non-selfsimilar viscous fluid jets]. Saratov: Izd-vo Saratov. un-ta, 1977, 220 p. [In Russian] 9. Velmisov P. A., Mizher U. J., Semenova E. P. AIP Conference Proceedings. 2018, vol. 2048, iss. 1, pp. 040012-1–040012-11. 10. Vel'misov P. A., Mizkher U. D., Semenova E. P. Differentsial'nye uravneniya i ikh prilozheniya v matematicheskom modelirovanii: materialy XIII Mezhdunar. nauch. konf. (Saransk, 12–16 iyulya 2017 g.) [Differential equations and their applications in mathematical modeling: proceedings of the III International scientific conference (Saransk, July 12-16, 2017)]. Saransk: SVMO, 2017, pp. 470–475. [In Russian]

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Дата обновления: 16.09.2020 14:16