Analytical solution and neutral curves of the stationary linear Rayleigh problem with rigid and mixed boundary conditions in cylindrical geometry
An analytical solution for the convective cells in a cylindrical geometry with rigid borders for the stationary linear Rayleigh problem is received. For a special case there were obtained expressions of distribution for perturbed velocity and temperature in cylindrical system coordinate with rigid b...
Saved in:
| Date: | 2017 |
|---|---|
| Main Authors: | , , |
| Format: | Article |
| Language: | Russian |
| Published: |
Інститут енергетичних машин і систем ім. А. М. Підгорного Національної академії наук України
2017
|
| Subjects: | |
| Online Access: | https://journals.uran.ua/jme/article/view/96728 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Energy Technologies & Resource Saving |
Institution
Energy Technologies & Resource Saving| id |
oai:ojs.journals.uran.ua:article-96728 |
|---|---|
| record_format |
ojs |
| spelling |
oai:ojs.journals.uran.ua:article-967282017-03-31T15:18:27Z Analytical solution and neutral curves of the stationary linear Rayleigh problem with rigid and mixed boundary conditions in cylindrical geometry Аналитические решения и нейтральные кривые стационарных линейных задач Рэлея для цилиндрических конвективных ячеек с твердыми и смешанными граничными условиями Андреева, О. Л. Костиков, А. О. Ткаченко, В. И. stationary linear of Rayleigh problem cylindrical geometry rigid or mixed boundary conditions analytic solution neutral curves УДК 632.5 стационарная линейная задача Рэлея цилиндрическая геометрия твердые или смешанные граничные условия аналитическое решение нейтральные кривые УДК 632.5 стаціонарна лінійна задача Релея циліндрична геометрія тверді або змішані граничні умови аналітичний розв’язок нейтральні криві УДК 632.5 An analytical solution for the convective cells in a cylindrical geometry with rigid borders for the stationary linear Rayleigh problem is received. For a special case there were obtained expressions of distribution for perturbed velocity and temperature in cylindrical system coordinate with rigid boundaries. Selected results can be useful in solving the problem of stationary Rayleigh solid boundaries in the rectangular coordinate system This distributions were compared to similar property for free convective cell for the main mode. In order to construct the neutral curves let’s use the solutions invariance with respect to the scale-shift transformation of the problem’s parameters. The term "invariance with respect to the scale-shift transformation" responds to the immutability of the solutions. On the basis of the analytical solutions analytical expressions are built for the neutral curves in the case of rigid or mixed boundary conditions. It is shown that those neutral curves correspond with sufficient precision to the ones numerically calculated by other authors. Получено аналитическое решение стационарной линейной задачи Рэлея для конвективной ячейки в цилиндрической геометрии с твердыми граничными условиями. На его основе построены аналитические выражения для нейтральных кривых в случае твердых и смешанных граничных условий. Показано, что нейтральные кривые с достаточной степенью точности соответствуют численным расчетам, полученным другими авторами. Отримано аналітичний розв’язок стаціонарної лінійної задачі Релея для конвективної комірки в циліндричній геометрії з твердими граничними умовами. На його основі побудовано аналітичні вирази для нейтральних кривих у випадку твердих і змішаних граничних умов. Показано, що нейтральні криві з достатнім ступенем точності відповідають чисельним розрахункам, отриманим іншими авторами Інститут енергетичних машин і систем ім. А. М. Підгорного Національної академії наук України 2017-03-24 Article Article application/pdf https://journals.uran.ua/jme/article/view/96728 Journal of Mechanical Engineering; Vol. 20 No. 1 (2017); 17-22 Проблемы машиностроения; Том 20 № 1 (2017); 17-22 Проблеми машинобудування; Том 20 № 1 (2017); 17-22 2709-2992 2709-2984 ru https://journals.uran.ua/jme/article/view/96728/92078 Copyright (c) 2017 О. Л. Андреева, А. О. Костиков, В. И. Ткаченко https://creativecommons.org/licenses/by-nd/4.0 |
| institution |
Energy Technologies & Resource Saving |
| baseUrl_str |
|
| datestamp_date |
2017-03-31T15:18:27Z |
| collection |
OJS |
| language |
Russian |
| topic |
stationary linear of Rayleigh problem cylindrical geometry rigid or mixed boundary conditions analytic solution neutral curves УДК 632.5 |
| spellingShingle |
stationary linear of Rayleigh problem cylindrical geometry rigid or mixed boundary conditions analytic solution neutral curves УДК 632.5 Андреева, О. Л. Костиков, А. О. Ткаченко, В. И. Analytical solution and neutral curves of the stationary linear Rayleigh problem with rigid and mixed boundary conditions in cylindrical geometry |
| topic_facet |
stationary linear of Rayleigh problem cylindrical geometry rigid or mixed boundary conditions analytic solution neutral curves УДК 632.5 стационарная линейная задача Рэлея цилиндрическая геометрия твердые или смешанные граничные условия аналитическое решение нейтральные кривые УДК 632.5 стаціонарна лінійна задача Релея циліндрична геометрія тверді або змішані граничні умови аналітичний розв’язок нейтральні криві УДК 632.5 |
| format |
Article |
| author |
Андреева, О. Л. Костиков, А. О. Ткаченко, В. И. |
| author_facet |
Андреева, О. Л. Костиков, А. О. Ткаченко, В. И. |
| author_sort |
Андреева, О. Л. |
| title |
Analytical solution and neutral curves of the stationary linear Rayleigh problem with rigid and mixed boundary conditions in cylindrical geometry |
| title_short |
Analytical solution and neutral curves of the stationary linear Rayleigh problem with rigid and mixed boundary conditions in cylindrical geometry |
| title_full |
Analytical solution and neutral curves of the stationary linear Rayleigh problem with rigid and mixed boundary conditions in cylindrical geometry |
| title_fullStr |
Analytical solution and neutral curves of the stationary linear Rayleigh problem with rigid and mixed boundary conditions in cylindrical geometry |
| title_full_unstemmed |
Analytical solution and neutral curves of the stationary linear Rayleigh problem with rigid and mixed boundary conditions in cylindrical geometry |
| title_sort |
analytical solution and neutral curves of the stationary linear rayleigh problem with rigid and mixed boundary conditions in cylindrical geometry |
| title_alt |
Аналитические решения и нейтральные кривые стационарных линейных задач Рэлея для цилиндрических конвективных ячеек с твердыми и смешанными граничными условиями |
| description |
An analytical solution for the convective cells in a cylindrical geometry with rigid borders for the stationary linear Rayleigh problem is received. For a special case there were obtained expressions of distribution for perturbed velocity and temperature in cylindrical system coordinate with rigid boundaries. Selected results can be useful in solving the problem of stationary Rayleigh solid boundaries in the rectangular coordinate system This distributions were compared to similar property for free convective cell for the main mode. In order to construct the neutral curves let’s use the solutions invariance with respect to the scale-shift transformation of the problem’s parameters. The term "invariance with respect to the scale-shift transformation" responds to the immutability of the solutions. On the basis of the analytical solutions analytical expressions are built for the neutral curves in the case of rigid or mixed boundary conditions. It is shown that those neutral curves correspond with sufficient precision to the ones numerically calculated by other authors. |
| publisher |
Інститут енергетичних машин і систем ім. А. М. Підгорного Національної академії наук України |
| publishDate |
2017 |
| url |
https://journals.uran.ua/jme/article/view/96728 |
| work_keys_str_mv |
AT andreevaol analyticalsolutionandneutralcurvesofthestationarylinearrayleighproblemwithrigidandmixedboundaryconditionsincylindricalgeometry AT kostikovao analyticalsolutionandneutralcurvesofthestationarylinearrayleighproblemwithrigidandmixedboundaryconditionsincylindricalgeometry AT tkačenkovi analyticalsolutionandneutralcurvesofthestationarylinearrayleighproblemwithrigidandmixedboundaryconditionsincylindricalgeometry AT andreevaol analitičeskierešeniâinejtralʹnyekrivyestacionarnyhlinejnyhzadačréleâdlâcilindričeskihkonvektivnyhâčeekstverdymiismešannymigraničnymiusloviâmi AT kostikovao analitičeskierešeniâinejtralʹnyekrivyestacionarnyhlinejnyhzadačréleâdlâcilindričeskihkonvektivnyhâčeekstverdymiismešannymigraničnymiusloviâmi AT tkačenkovi analitičeskierešeniâinejtralʹnyekrivyestacionarnyhlinejnyhzadačréleâdlâcilindričeskihkonvektivnyhâčeekstverdymiismešannymigraničnymiusloviâmi |
| first_indexed |
2025-07-17T12:01:54Z |
| last_indexed |
2025-07-17T12:01:54Z |
| _version_ |
1850411690833739776 |