PSI - Issue 40

ScienceDirect Structural Integrity Procedia 00 (2022) 000 – 000 Structural Integrity Procedia 00 (2022) 000 – 000 Available online at www.sciencedirect.com Available online at www.sciencedirect.com Sci nceDire t Available online at www.sciencedirect.com ScienceDirect

www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia

Procedia Structural Integrity 40 (2022) 82–89

15th International Conference on Mechanics, Resource and Diagnostics of Materials and Structures Isothermal shear flows of viscous vortex fluids in a thin slit 15th International Conference on Mechanics, Resource and Diagnostics of Materials and Stru tures Isothermal shear flows of viscous vortex fluids in a thin slit

Natalya V. Burmasheva a,b, *, Evgeniy Yu. Prosviryakov a,b a Institute of Engineering Science UB RAS, 34 Komsomolskaya St., Ekaterinburg, 620049, Russia b B. N. Yeltsin Ural Federal University, 19 Mira St., Ekaterinburg, 620002, Russia Natalya V. Burmasheva a,b, *, Evgeniy Yu. Prosviryakov a,b a Institute of Engineering Science UB RAS, 34 Komsomolskaya St., Ekaterinburg, 620049, Russia b B. N. Yeltsin Ural F deral University, 19 Mira St., Ekaterinburg, 620002, Russia

© 2022 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the scientific committee of the15th International Conference on Mechanics, Resources and Diagnostics of Materials and Structures. Abstract The paper presents a new exact solution describing the isobaric isothermal shear flow of a viscous incompressible fluid in a horizontal layer with slippage. It is shown that the resulting system of equations is overdetermined. A method is proposed for solving such systems using classes of exact solutions of a certain structure. It is also shown that the constructed exact polynomial solution can describe the occurrence of counterflows in a fluid, as well as stress field stratification. © 2022 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the scientific committee of the15th International Conference on Mechanics, Resource and Diagnostics of Materials and Structures. Keywords: viscous incompressible fluid; isobaric isothermal flow; shear flow; Navier-Stokes equations; exact solution; overdetermined system; consistency condition 1. Introduction Viscous fluid flows are an important part of many industrial processes. As a rule, we speak of the redistribution of thermal fields or various impurities as a result of the motion of a fluid heat carrier. In this case, the properties of each of the fields (thermal, concentration, etc.) at an arbitrary moment of a technological process are largely determined by the properties of the flow of the viscous fluid participating in this process. In addition, the flow of a viscous fluid in technical devices can often be attributed to the class of stratified (shear) flows, which are characterized by the predominance of two components of the velocity vector over the third one. In Abstract The paper presents a new exact solution describing the isobaric isothermal shear flow of a viscous incompressible fluid in a horizontal layer with slippage. It is sh wn that the result ng system of equations is verdetermined. A method is proposed for s lving such systems us ng classes of exact solutions of a certain structur . It is al o shown that the construc ed exact polynomial ution can de cribe the oc urrence of counterflow in a fluid, as well as stres field tratification. © 2022 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review u der re ponsibility of scientific committe of the15th Int rnational Co ference on Mechanics, Resource and Diagnostics of Materials and S ructur s. Keywords: viscous incompressible fl id; isobaric isothermal flow; shear flow; Navier-Stokes equations; exact solution; overdetermined system; consistency conditio 1. Introduction Viscous fluid flows are an important part of many industrial processes. As a rule, we speak of the redistribution of thermal fields or various impurities as a result of the motion of a fluid heat carrier. In thi case, the properties of each of the fields (thermal, concentration, etc.) at an arbitrary moment of a technological process are largely d termined by t properties of the flow of the viscous fluid participating in this process. In addition, the flow of a viscous fluid in technical devices can often be attributed to the class of stratified (shear) flows, which are characterized by the predomina ce of two components of the veloci y vector over the th r one. In

* Corresponding author. Tel.: +7-343-375-3576. E-mail address: nat_burm@mail.ru * Corresponding author. Tel.: +7-343-375-3576. E-mail ad ress: nat_burm@mail.ru

2452-3216 © 2022 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the scientific committee of the15th International Conference on Mechanics, Resource and Diagnostics of Materials and Structures. 2452-3216 © 2022 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review u der re ponsibility of scientific committe of the15th Int rnational C ference o Mechanics, Resource and Diagnostics of Mate ials and Structures.

2452-3216 © 2022 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the scientific committee of the15th International Conference on Mechanics, Resources and Diagnostics

of Materials and Structures. 10.1016/j.prostr.2022.04.010