Heat convection of viscous incompressible liquid in a cylindric elementary convection cell with a conical cavity bottom and rigid boundary conditions

Authors

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

Keywords:

cylindric elementary convection cell, heat convection, conical cavity, solid boundary conditions, viscous incompressible liquid, Fujiwhara effect

Abstract

There was studied the problem of heat convection of viscous incompressible liquid in a cylindrical elementary convection cell with a conical cavity bottom and  rigid boundary conditions. For a special case there were obtained expressions of distribution for perturbed velocity and temperature in cylindrical system coordinate with rigid boundaries. It shows the diagram of a cylindrical unit cell with convective conically recessed bottom in a layer of a viscous, incompressible fluid and rigid boundary conditions. Defined spatial field distribution of flow velocities in a cell with a conically recessed bottom and rigid boundary conditions on the surface z = 1 and z = 0. Top elementary convective cell borders on a horizontal array of metallic heat dissipating layer thickness, from below - from a horizontal layer heat input medium, temperature gradient is maintained constant thickness. Stokes' functions were constructed for cylindrical convection cell as well as for the conical cavity in the cell bottom. Basing on Fujiwhara effect there were obtained Stokes streamline model distributions in the cylindrical elementary convection cell with conical cavity bottom and solid boundary conditions and disturbed temperature. In this paper we consider the problem of convective heat and mass transfer in a cylindrical elementary convection cell with a conical depression heated from below

Author Biographies

А. О. Костиков, AN Podgorny Institute of Engineering Problems of the National Academy of Sciences of Ukraine, Kharkov V. N. Karazin Kharkiv National University

Doctor of Technical Sciences

В. И. Ткаченко, National Science Center Kharkov Institute of Physics and Technology V. N. Karazin Kharkiv National University

Doctor of Physical and Mathematical Sciences

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Published

2017-06-30

Issue

Vol. 20 No. 2 (2017)

Section

Aerohydrodynamics and heat-mass transfer

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

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