Pub Date : 2024-08-28DOI: 10.1134/s1995080224602479
Giovanni Migliaccio, Hovik A. Matevossian
Abstract
In this paper, we consider a biharmonic problem with Steklov-type boundary conditions on one part of the boundary and with the Farwig condition on the other part. For this problem, questions of uniqueness of solutions are studied, and in the case of non-uniqueness, provided that the weighted Dirichlet integral is bounded, the exact number of linear independent solutions to the problem under consideration is established. Using the variational principle, uniqueness (non-uniqueness) theorems are obtained, as well as exact formulas for calculating the dimension of the space of solutions depending on the value of the parameter included in the weighted Dirichlet integral.
{"title":"Solution of the Biharmonic Problem with the Steklov-type and Farwig Boundary Conditions","authors":"Giovanni Migliaccio, Hovik A. Matevossian","doi":"10.1134/s1995080224602479","DOIUrl":"https://doi.org/10.1134/s1995080224602479","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In this paper, we consider a biharmonic problem with Steklov-type boundary conditions on one part of the boundary and with the Farwig condition on the other part. For this problem, questions of uniqueness of solutions are studied, and in the case of non-uniqueness, provided that the weighted Dirichlet integral is bounded, the exact number of linear independent solutions to the problem under consideration is established. Using the variational principle, uniqueness (non-uniqueness) theorems are obtained, as well as exact formulas for calculating the dimension of the space of solutions depending on the value of the parameter included in the weighted Dirichlet integral.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217032","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-28DOI: 10.1134/s1995080224602145
A. A. Gubaidullin, O. Yu. Boldyreva, D. N. Dudko
Abstract
The transmission and reflection of a pulse wave in a porous medium with a layer of a fractured porous medium under normal and oblique incidence is numerically investigated. The study was carried out using a two-velocity model of a porous medium and a three-velocity model of a fractured porous medium. ‘‘Opened pores’’ condition was used on the ‘‘porous medium–fractured porous medium’’ interface. The problem is considered in a two-dimensional formulation. The features of this wave process are revealed.
{"title":"Wave Interaction with Fractured Porous Layer in Porous Medium","authors":"A. A. Gubaidullin, O. Yu. Boldyreva, D. N. Dudko","doi":"10.1134/s1995080224602145","DOIUrl":"https://doi.org/10.1134/s1995080224602145","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The transmission and reflection of a pulse wave in a porous medium with a layer of a fractured porous medium under normal and oblique incidence is numerically investigated. The study was carried out using a two-velocity model of a porous medium and a three-velocity model of a fractured porous medium. ‘‘Opened pores’’ condition was used on the ‘‘porous medium–fractured porous medium’’ interface. The problem is considered in a two-dimensional formulation. The features of this wave process are revealed.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"34 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217075","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-28DOI: 10.1134/s1995080224602200
R. I. Ibyatov, F. G. Akhmadiev
Abstract
The mathematical modeling of the non-isothermal flow of two-phase media in curved channels and pipes of complex geometric shapes is considered. Simplified equations of motion of a two-phase medium, taking into account the flow characteristics, written in an orthogonal coordinate system associated with the flow region, are solved by the method of equal flow surfaces. An algorithm for calculating the flow is constructed for the implementation of a computational experiment. This takes into account changes in the physical characteristics of the two-phase medium depending on temperature. Numerical calculations have been performed for channels of parabolic and conical shapes, taking into account changes in the effective viscosity of the medium from temperature, the initial section of the flow, and the influence of the centrifugal force field. Based on the conducted computational experiment, various flow regimes and the influence of various parameters on the hydrodynamic situation in the flow region are studied.
{"title":"Mathematical Modeling of Non-isothermal Flow of Two-phase Media in Curved Channels","authors":"R. I. Ibyatov, F. G. Akhmadiev","doi":"10.1134/s1995080224602200","DOIUrl":"https://doi.org/10.1134/s1995080224602200","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The mathematical modeling of the non-isothermal flow of two-phase media in curved channels and pipes of complex geometric shapes is considered. Simplified equations of motion of a two-phase medium, taking into account the flow characteristics, written in an orthogonal coordinate system associated with the flow region, are solved by the method of equal flow surfaces. An algorithm for calculating the flow is constructed for the implementation of a computational experiment. This takes into account changes in the physical characteristics of the two-phase medium depending on temperature. Numerical calculations have been performed for channels of parabolic and conical shapes, taking into account changes in the effective viscosity of the medium from temperature, the initial section of the flow, and the influence of the centrifugal force field. Based on the conducted computational experiment, various flow regimes and the influence of various parameters on the hydrodynamic situation in the flow region are studied.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"427 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217080","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-28DOI: 10.1134/s1995080224602224
M. Kh. Khairullin, E. R. Badertdinova
Abstract
Unsteady filtration of a Bingham non-Newtonian fluid to a horizontal well is considered. The experimental results show that when such liquids flow in porous media at low pressure gradients, deviations from the linear Darcy law appear. A feature of the movement of Bingham non-Newtonian fluids in a porous medium is the fact that filtration becomes noticeable only after the pressure gradient reaches a certain critical value—the limiting pressure gradient. The formulation of the inverse coefficient problem for determining filtration parameters during the flow of Bingham non-Newtonian fluid to a horizontal well is given. Pressure change curves measured at the well are used as initial information. To numerically solve the inverse coefficient problem, a computational algorithm based on regularization methods is proposed.
{"title":"Numerical Solution of the Inverse Problem of Non-stationary Filtration of Bingham Non-Newtonian Fluid to a Horizontal Well","authors":"M. Kh. Khairullin, E. R. Badertdinova","doi":"10.1134/s1995080224602224","DOIUrl":"https://doi.org/10.1134/s1995080224602224","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Unsteady filtration of a Bingham non-Newtonian fluid to a horizontal well is considered. The experimental results show that when such liquids flow in porous media at low pressure gradients, deviations from the linear Darcy law appear. A feature of the movement of Bingham non-Newtonian fluids in a porous medium is the fact that filtration becomes noticeable only after the pressure gradient reaches a certain critical value—the limiting pressure gradient. The formulation of the inverse coefficient problem for determining filtration parameters during the flow of Bingham non-Newtonian fluid to a horizontal well is given. Pressure change curves measured at the well are used as initial information. To numerically solve the inverse coefficient problem, a computational algorithm based on regularization methods is proposed.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"297 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217086","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-28DOI: 10.1134/s1995080224602261
D. Yu. Legostaev, S. P. Rodionov
Abstract
We consider two-dimensional single-phase fluid flow of an incompressible fluid in a fractured porous medium, which is located inside a square computational domain. The fractures had a random position and orientation, and the fracture length distribution follows a power law. Fracture networks are simulated using the discrete-fracture model. Calculations were performed for fracture network realizations created by multiple random generations. Fluid flows between opposite boundaries of the computational domain (line source and sink) and between vertical wells (point source and sink) are considered. The influence of the type of source and sink on the percolation probability is determined. The dependence of the flow rate between production and injection wells on the fracture network structure was investigated. The flow between the opposite boundaries of the computational domain is considered. For this case, the numerical dependence of the equivalent permeability of the fractured porous medium on the percolation parameter was approximated by an analytical piecewise function. This approximation was used to estimate fluid flow rates between vertical wells.
{"title":"Numerical Investigation of the Structure of Fracture Network Impact on Interwell Conductivity","authors":"D. Yu. Legostaev, S. P. Rodionov","doi":"10.1134/s1995080224602261","DOIUrl":"https://doi.org/10.1134/s1995080224602261","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>We consider two-dimensional single-phase fluid flow of an incompressible fluid in a fractured porous medium, which is located inside a square computational domain. The fractures had a random position and orientation, and the fracture length distribution follows a power law. Fracture networks are simulated using the discrete-fracture model. Calculations were performed for fracture network realizations created by multiple random generations. Fluid flows between opposite boundaries of the computational domain (line source and sink) and between vertical wells (point source and sink) are considered. The influence of the type of source and sink on the percolation probability is determined. The dependence of the flow rate between production and injection wells on the fracture network structure was investigated. The flow between the opposite boundaries of the computational domain is considered. For this case, the numerical dependence of the equivalent permeability of the fractured porous medium on the percolation parameter was approximated by an analytical piecewise function. This approximation was used to estimate fluid flow rates between vertical wells.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"6 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217087","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-28DOI: 10.1134/s1995080224602297
N. G. Musakaev, S. L. Borodin, D. S. Belskikh
Abstract
A mathematical model of non-isothermal filtration of methane, carbon dioxide and water is constructed based on the methods and equations of multiphase media mechanics considering the replacement of methane in the gas hydrate with carbon dioxide. The equations of the mathematical model and the methodology for their numerical solution are presented. The numerical solutions for one-dimensional plane-parallel approximation are constructed for the problem of injecting carbon dioxide into a reservoir initially saturated with methane and its hydrate. Those solutions describe the distributions in the reservoir of pressure, temperature, mass concentrations of gas phase components and saturations of methane and carbon dioxide hydrates.
{"title":"Methodology for Calculating the Parameters of Non-isothermal Filtration Considering the CO $${}_{mathbf{2}}$$ –CH $${}_{mathbf{4}}$$ Replacement in Methane Hydrate","authors":"N. G. Musakaev, S. L. Borodin, D. S. Belskikh","doi":"10.1134/s1995080224602297","DOIUrl":"https://doi.org/10.1134/s1995080224602297","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>A mathematical model of non-isothermal filtration of methane, carbon dioxide and water is constructed based on the methods and equations of multiphase media mechanics considering the replacement of methane in the gas hydrate with carbon dioxide. The equations of the mathematical model and the methodology for their numerical solution are presented. The numerical solutions for one-dimensional plane-parallel approximation are constructed for the problem of injecting carbon dioxide into a reservoir initially saturated with methane and its hydrate. Those solutions describe the distributions in the reservoir of pressure, temperature, mass concentrations of gas phase components and saturations of methane and carbon dioxide hydrates.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"37 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217090","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-28DOI: 10.1134/s1995080224602285
I. V. Morenko
Abstract
The dynamics of two gas bubbles rising in a stagnant viscous liquid is studied. The mathematical model is based on the laws of conservation of mass, momentum and energy, taking into account the compressibility of media. The gas is assumed to be calorically perfect. To trace the gas–liquid interface, the volume of fluid method is used. The solution to the problem is carried out using the finite volume method. The evolution of the bubble shape during the process of ascent and hydrodynamic interaction is shown. The change in the bubble shapes occurs under the influence of buoyancy force, drag force, viscous force, inertia force, and surface tension force. The results of the test calculations are in good agreement with the known data of other authors. The mechanism of coalescence of bubbles is described in the case of their movement one after another, when one bubble falls into the region of the hydrodynamic wake of another. Dependencies of bubble volume and temperature change on time are established.
{"title":"Interaction of Two Gas Bubbles Rising One after Another in a Liquid","authors":"I. V. Morenko","doi":"10.1134/s1995080224602285","DOIUrl":"https://doi.org/10.1134/s1995080224602285","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The dynamics of two gas bubbles rising in a stagnant viscous liquid is studied. The mathematical model is based on the laws of conservation of mass, momentum and energy, taking into account the compressibility of media. The gas is assumed to be calorically perfect. To trace the gas–liquid interface, the volume of fluid method is used. The solution to the problem is carried out using the finite volume method. The evolution of the bubble shape during the process of ascent and hydrodynamic interaction is shown. The change in the bubble shapes occurs under the influence of buoyancy force, drag force, viscous force, inertia force, and surface tension force. The results of the test calculations are in good agreement with the known data of other authors. The mechanism of coalescence of bubbles is described in the case of their movement one after another, when one bubble falls into the region of the hydrodynamic wake of another. Dependencies of bubble volume and temperature change on time are established.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"59 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217091","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-28DOI: 10.1134/s1995080224602546
V. I. Zubov
Abstract
The work analyzes one optimal control problem that arises in nanoelectronics. It is shown that the use of an approximate expression for the variation of electron density leads to an incorrect value for the gradient of the cost functional. It is demonstrated that the formulated optimal control problem is incorrect. For the correct formulation of the optimal control problem, other cost functions should be used.
{"title":"On One Optimization Problem in Nanoelectronics","authors":"V. I. Zubov","doi":"10.1134/s1995080224602546","DOIUrl":"https://doi.org/10.1134/s1995080224602546","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The work analyzes one optimal control problem that arises in nanoelectronics. It is shown that the use of an approximate expression for the variation of electron density leads to an incorrect value for the gradient of the cost functional. It is demonstrated that the formulated optimal control problem is incorrect. For the correct formulation of the optimal control problem, other cost functions should be used.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"37 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217033","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-28DOI: 10.1134/s1995080224602194
T. S. Guseva
Abstract
The jet impact process during the nonspherical bubble collapse near a local bump on a solid wall has been studied in detail using the CIP-CUP method to solve the Euler equations. Three scenarios were considered, the first of which corresponds to a nearly plane wall compared to the bubble size, and the other two correspond to the bubble-sized local bump. In all cases, the distance from the impact location to the wall and the jet tip diameter are close, the jet velocity is about 100 m/s. The main difference between the considered scenarios is the initial zone of contact of the jet with the opposite bubble side. Namely, it is a single point in the first case, and in the other two cases it is a bowl-shaped area and an annular area with the formation of a tip bubble. The latter two scenarios have been found to result in significantly higher wall pressure, as well as larger loaded area and load duration.
{"title":"Jet Impact During Bubble Collapse Near a Local Bump on a Solid Wall","authors":"T. S. Guseva","doi":"10.1134/s1995080224602194","DOIUrl":"https://doi.org/10.1134/s1995080224602194","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The jet impact process during the nonspherical bubble collapse near a local bump on a solid wall has been studied in detail using the CIP-CUP method to solve the Euler equations. Three scenarios were considered, the first of which corresponds to a nearly plane wall compared to the bubble size, and the other two correspond to the bubble-sized local bump. In all cases, the distance from the impact location to the wall and the jet tip diameter are close, the jet velocity is about 100 m/s. The main difference between the considered scenarios is the initial zone of contact of the jet with the opposite bubble side. Namely, it is a single point in the first case, and in the other two cases it is a bowl-shaped area and an annular area with the formation of a tip bubble. The latter two scenarios have been found to result in significantly higher wall pressure, as well as larger loaded area and load duration.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"26 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217076","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-28DOI: 10.1134/s1995080224602315
A. D. Nizamova, V. N. Kireev, S. F. Urmancheev
Abstract
Issues related to transient regimes of fluid flow in channels with different cross sections are a priority when solving problems of hydrodynamics. Currently, research related to the influence of heat exchange on the stability of fluid flow in processes in which the change in viscosity with temperature cannot be neglected has become particularly relevant. This article examines some features of the loss of stability of a laminar fluid flow with an exponential dependence of viscosity on temperature in an annular channel with a given temperature regime on its walls. For this purpose, the generalized Orr–Sommerfeld equation was derived, which was eventually written in relation to the stream function. A numerical study of the corresponding boundary value problem was carried out using the spectral method based on Chebyshev polynomials. It was shown that taking into account the effect of temperature on the viscosity of the liquid, which implies its non-uniform distribution over the cross section of the channel, leads to a decrease in the critical Reynolds number, which is consistent with the results of previous studies. In particular, as previously noted, for a narrow channel and a small thermoviscosity parameter, the spectrum of eigenvalues is identical to the spectrum for an isothermal flow in a flat channel. A change in the relative channel width and an increase in the thermoviscosity parameter leads to a significant restructuring of the structure of the eigenvalue spectra of the generalized Orr–Sommerfeld equation. As a result of the studies carried out in the presented work, the dependencies of the critical Reynolds number on the exponential factor or, in other words, the thermoviscosity parameter, which characterizes the intensity of the change in viscosity with increasing temperature, and on the parameter determining the ratio of the width of the annular channel to the radius of the inner cylindrical surface were constructed. It has been established that with increasing parameter of the relative channel width, the value of the critical Reynolds number changes non-monotonically, and its minimum value depends on the specific liquid. The latter circumstance can serve as a theoretical justification for carrying out optimization calculations when modeling technological processes. The dependence of the critical Reynolds number on the thermoviscosity parameter has a form close to a decreasing exponential function for all sizes of annular channels.
{"title":"The Influence of the Annular Gap Thickness on the Critical Reynolds Number During the Flow of Thermoviscous Liquids","authors":"A. D. Nizamova, V. N. Kireev, S. F. Urmancheev","doi":"10.1134/s1995080224602315","DOIUrl":"https://doi.org/10.1134/s1995080224602315","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Issues related to transient regimes of fluid flow in channels with different cross sections are a priority when solving problems of hydrodynamics. Currently, research related to the influence of heat exchange on the stability of fluid flow in processes in which the change in viscosity with temperature cannot be neglected has become particularly relevant. This article examines some features of the loss of stability of a laminar fluid flow with an exponential dependence of viscosity on temperature in an annular channel with a given temperature regime on its walls. For this purpose, the generalized Orr–Sommerfeld equation was derived, which was eventually written in relation to the stream function. A numerical study of the corresponding boundary value problem was carried out using the spectral method based on Chebyshev polynomials. It was shown that taking into account the effect of temperature on the viscosity of the liquid, which implies its non-uniform distribution over the cross section of the channel, leads to a decrease in the critical Reynolds number, which is consistent with the results of previous studies. In particular, as previously noted, for a narrow channel and a small thermoviscosity parameter, the spectrum of eigenvalues is identical to the spectrum for an isothermal flow in a flat channel. A change in the relative channel width and an increase in the thermoviscosity parameter leads to a significant restructuring of the structure of the eigenvalue spectra of the generalized Orr–Sommerfeld equation. As a result of the studies carried out in the presented work, the dependencies of the critical Reynolds number on the exponential factor or, in other words, the thermoviscosity parameter, which characterizes the intensity of the change in viscosity with increasing temperature, and on the parameter determining the ratio of the width of the annular channel to the radius of the inner cylindrical surface were constructed. It has been established that with increasing parameter of the relative channel width, the value of the critical Reynolds number changes non-monotonically, and its minimum value depends on the specific liquid. The latter circumstance can serve as a theoretical justification for carrying out optimization calculations when modeling technological processes. The dependence of the critical Reynolds number on the thermoviscosity parameter has a form close to a decreasing exponential function for all sizes of annular channels.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"26 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217093","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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