Analytical solution and neutral curves of the stationary linear Rayleigh problem with rigid and mixed boundary conditions in cylindrical geometry

• Main Authors: Андреева, О. Л., Костиков, А. О., Ткаченко, В. И.
• Format: Article
• Language: Russian
• Published: Інститут енергетичних машин і систем ім. А. М. Підгорного Національної академії наук України 2017
• Subjects: 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; стаціонарна лінійна задача Релея; циліндрична геометрія; тверді або змішані граничні умови; аналітичний розв’язок; нейтральні криві
• Online Access: https://journals.uran.ua/jme/article/view/96728

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.