PSI - Issue 65

Available online at www.sciencedirect.com Available online at www.sciencedirect.com ScienceDirect Structural Integrity Procedia 00 (2024) 000–000 Available online at www.sciencedirect.com ScienceDirect Structural Integrity Procedia 00 (2024) 000–000

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

ScienceDirect

Procedia Structural Integrity 65 (2024) 185–190

The 17th International Conference on MECHANICS, RESOURCE AND DIAGNOSTICS OF MATERIALS AND STRUCTURES (MRDMS 2023) Exact solutions of the Navier-Stokes equations in the Boussinesq approximation for describing the flow of binary fluids E.Yu. Prosviryakov a,b,c, * , O.A. Ledyankina c , L.S. Goruleva a,b a Institute of Engineering Science, Ural Branch of the RAS, 34 Komsomolskaya St., Ekaterinburg, 620049, Russia b Ural Federal University, 19 Mira St., Ekaterinburg, 620002, Russia c Tupolev Kazan National Research Technical University, 10 Karla Marksa St., Kazan, 420111, Russia The 17th International Conference on MECHANICS, RESOURCE AND DIAGNOSTICS OF MATERIALS AND STRUCTURES (MRDMS 2023) Exact solutions of the Navier-Stokes equations in the Boussinesq approximation for describing the flow of binary fluids E.Yu. Prosviryakov a,b,c, * , O.A. Ledyankina c , L.S. Goruleva a,b a Institute of Engineering Science, Ural Branch of the RAS, 34 Komsomolskaya St., Ekaterinburg, 620049, Russia b Ural Federal University, 19 Mira St., Ekaterinburg, 620002, Russia c Tupolev Kazan National Research Technical University, 10 Karla Marksa St., Kazan, 420111, Russia An exact solution is proposed for describing creeping convective flows of binary fluids. The velocity field is quadratically nonlinear in two spatial coordinates (horizontal or longitudinal). The coefficients of the forms depend on the third coordinate (vertical or transverse) and time. The pressure field, the concentration field, and the mass force field are nonlinear forms of the fourth order. Linear differential equations of the heat conductivity type and gradient equations for describing hydrodynamic fields are given. © 2024 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 MRDMS 2023 organizers Keywords: exact solutions, convection, Oberbeck–Boussinesq equations, dissipative function, diffusion, binary fluid; © 2024 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 MRDMS 2023 organizers Abstract Abstract An exact solution is proposed for describing creeping convective flows of binary fluids. The velocity field is quadratically nonlinear in two spatial coordinates (horizontal or longitudinal). The coefficients of the forms depend on the third coordinate (vertical or transverse) and time. The pressure field, the concentration field, and the mass force field are nonlinear forms of the fourth order. Linear differential equations of the heat conductivity type and gradient equations for describing hydrodynamic fields are given. © 2024 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 MRDMS 2023 organizers Keywords: exact solutions, convection, Oberbeck–Boussinesq equations, dissipative function, diffusion, binary fluid; Convective motions of liquids can be induced by various force fields [Aristov et al. (2016), Andreev et al. (2009)]. Traditionally, thermal convection and thermal diffusion in liquids are studied. Exact solutions for the equations of natural convection and thermal diffusion are found in the Lin-Sidorov-Aristov class [Aristov et al. (2016), Aristov et al. (2009), Lin et al. (1958), Sidorov et al. (1989), Aristov et al. (1990)]. The use of the Lin Sidorov-Aristov family allows one to describe shear and layered convective flows for thermal and concentration Convective motions of liquids can be induced by various force fields [Aristov et al. (2016), Andreev et al. (2009)]. Traditionally, thermal convection and thermal diffusion in liquids are studied. Exact solutions for the equations of natural convection and thermal diffusion are found in the Lin-Sidorov-Aristov class [Aristov et al. (2016), Aristov et al. (2009), Lin et al. (1958), Sidorov et al. (1989), Aristov et al. (1990)]. The use of the Lin Sidorov-Aristov family allows one to describe shear and layered convective flows for thermal and concentration 1. Introduction 1. Introduction

* Corresponding author. Tel.: +7-982-654-5223. E-mail address: evgen_pros@mail.ru * Corresponding author. Tel.: +7-982-654-5223. E-mail address: evgen_pros@mail.ru

2452-3216 © 2024 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 MRDMS 2023 organizers 2452-3216 © 2024 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 MRDMS 2023 organizers

2452-3216 © 2024 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 MRDMS 2023 organizers 10.1016/j.prostr.2024.11.029