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

Authors

  • О. Л. Андреева AN Podgorny Institute of Engineering Problems of the National Academy of Sciences of Ukraine, Kharkov, Ukraine
  • А. О. Костиков National Science Center "Kharkov Institute of Physics and Technology" NAS of Ukraine, Ukraine
  • В. И. Ткаченко V. N. Karazina Kharkiv National University, Ukraine

Keywords:

stationary linear of Rayleigh problem, cylindrical geometry, rigid or mixed boundary conditions, analytic solution, neutral curves

Abstract

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. 

Author Biographies

А. О. Костиков, National Science Center "Kharkov Institute of Physics and Technology" NAS of Ukraine

Doctor of Technical Sciences

В. И. Ткаченко, V. N. Karazina Kharkiv National University

Doctor of Physical and Mathematical Sciences

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Published

2017-03-24

Issue

Vol. 20 No. 1 (2017)

Section

Heat transfer in engineering constructions

License

Copyright (c) 2017 О. Л. Андреева, А. О. Костиков, В. И. Ткаченко

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