ANALYTICAL SOLUTION AND NEUTRAL CURVES OF THE STATIONARY LINEAR RAYLEIGH PROBLEM WITH RIGID OR MIXED BOUNDARY CONDITIONS IN CYLINDRICAL GEOMETRY
AbstractOn the basis of the Navier-Stokes equations in the Boussinesq approximation in the linear approximation the classical problem of Rayleigh, dedicated to the study of stable stationary solutions to the horizontal plane layer of a viscous, incompressible fluid heated from below in the case of execution on the upper and lower boundaries of the layer of solid boundary conditions is considered. The analytical solutions describing the perturbed velocity and temperature of the fluid in a cylindrical convection cell with solid boundary conditions are obtained. The obtained analytical solution to build similar solutions of the problem with mixed boundary conditions is used. The analytical expressions for the neutral curves in the case of solid and mixed boundary conditions based on the obtained solutions are built. A comparison of the analytically constructed neutral curves with numerical simulations obtained by other authors is carried out. The derived analytical expressions for the neutral curves of solid and mixed boundary conditions with sufficient accuracy correspond to the numerical calculations is shown.
Chandrasekhar S. Hydrodynamic and hydromagnetic stability, 1970. – 657 p.
Neklyudov I.M., Borts B.V. Tkachenko V.I. Opisanie Lengmurovskih cirkulyaciy uporyadochennim naborom konvektivnih kubicheskih yacheek // Prikladnaya gidromekhanika. – 2012. – Т. 14(86). – No.2. – S.29–40.
Shchuka А.А. Nanoelektronika. – M.: Binom. Laboratoriya znaniy, 2012. – 342 s.
Sazhin B.S., Reutskiy V.А. Sushka i promivka tekstilnih materialov: teoriya i raschet processov. – М.: Legpromizdat, 1990. – 224 s.
Muller G. Virashchivanie kristalov iz rasplava. – M.: Mir, 1991. – 143 s.
Rykalin N.N., Uglov А.А, Кокоrа А.N. Lazernaya obrabotka materialov. – М.: Мashinostroejnije, 1975. – 296 s.
Gershuny G.Z., Zhuhovickiy E.M. Convective stability of incompressible fluid. – Мoscow: Nauka, 1972. – 393 p.
Strutt J. W. (Lord Rау1еigh) // Phil. Mag. – 1916. – Vol. 32. – P. 529 – 546.
Bozbiei L., Borts B., Kazarinov Y., Kostikov A., Tkachenko V. Experimental Study of Liquid Movement in Free Elementary Convective Sells // Energetika. – 2015. – T.61. – No.2. – P. 45 – 56.
Patochkina О.L., Borts B.V., Tkachenko V.I. Elementary Convection Cell in the Horizontal Layer of Viscous Incompressible Liquid with Rigid and Mixed Boundary Conditions // East Eur. J. Phys. – 2015. – Vol. 2. – No. 1. – P. 23 – 31.
Bozbey L.S., Borts B.V., Kostikov A.O., Tkachenko V.I. Formation of Elementary Convective Cell in Horizontal Layer of Viscous Incompressible Fluid // East Eur. J. Phys. – 2014. – Vol. 1. – No.4. – P. 49 – 56.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).