On the onset of instabilities in a Bénard-Marangoni problem in an annular domain with temperature gradient
This manuscript addresses the linear stability analysis of a thermoconvective problem in an annular domain. The flow is heated from below, with a linear decreasing horizontal temperature profile from the inner to the outer wall. The top surface of the domain is open to the atmosphere and the two lat...
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VINCA Institute of Nuclear Sciences
2017-01-01
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doaj-b77321de9dc44d9dabb8ca179c5218f62021-01-02T01:47:13ZengVINCA Institute of Nuclear SciencesThermal Science0354-98362334-71632017-01-0121suppl. 358559610.2298/TSCI160628277H0354-98361600277HOn the onset of instabilities in a Bénard-Marangoni problem in an annular domain with temperature gradientHoyas Sergio0Ianiro Andrea1Perez-Quiles María J.2Fajardo Pablo3Universitat Politécnica de Valéncia, Instituto Universitario de Matemática Pura y Aplicada, Valéncia, SpainUniversidad Carlos III de Madrid, Aerospace Engineering Group, Madrid, SpainUniversitat Politécnica de Valéncia, Instituto Universitario de Matemática Pura y Aplicada, Valéncia, SpainUniversidad Carlos III de Madrid, Aerospace Engineering Group, Madrid, SpainThis manuscript addresses the linear stability analysis of a thermoconvective problem in an annular domain. The flow is heated from below, with a linear decreasing horizontal temperature profile from the inner to the outer wall. The top surface of the domain is open to the atmosphere and the two lateral walls are adiabatic. The effects of several parameters in the flow are evaluated. Three different values for the ratio of the momentum diffusivity and thermal diffusivity are considered: relatively low Prandtl number (Pr = 1), intermediate Prandtl number (Pr = 5) and high Prandtl number (ideally Pr → ∞ , namely Pr = 50). The thermal boundary condition on the top surface is changed by imposing different values of the Biot number, Bi. The influence of the aspect ratio (Γ) is assessed for through by studying several aspect ratios, Γ. The study has been performed for two values of the Bond number (namely Bo = 5 and 50), estimating the perturbation given by thermocapillarity effects on buoyancy effects. Different kinds of competing solutions appear on localized zones of the Γ-Bi plane. The boundaries of these zones are made up of co-dimension two points. Co-dimension two points are found to be function of Bond number, Marangoni number and boundary conditions but to be independent on the Prandtl number.http://www.doiserbia.nb.rs/img/doi/0354-9836/2017/0354-98361600277H.pdfMarangoni problemThermocapillary convectionLinear stabilityBuoyancy Effects |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Hoyas Sergio Ianiro Andrea Perez-Quiles María J. Fajardo Pablo |
spellingShingle |
Hoyas Sergio Ianiro Andrea Perez-Quiles María J. Fajardo Pablo On the onset of instabilities in a Bénard-Marangoni problem in an annular domain with temperature gradient Thermal Science Marangoni problem Thermocapillary convection Linear stability Buoyancy Effects |
author_facet |
Hoyas Sergio Ianiro Andrea Perez-Quiles María J. Fajardo Pablo |
author_sort |
Hoyas Sergio |
title |
On the onset of instabilities in a Bénard-Marangoni problem in an annular domain with temperature gradient |
title_short |
On the onset of instabilities in a Bénard-Marangoni problem in an annular domain with temperature gradient |
title_full |
On the onset of instabilities in a Bénard-Marangoni problem in an annular domain with temperature gradient |
title_fullStr |
On the onset of instabilities in a Bénard-Marangoni problem in an annular domain with temperature gradient |
title_full_unstemmed |
On the onset of instabilities in a Bénard-Marangoni problem in an annular domain with temperature gradient |
title_sort |
on the onset of instabilities in a bénard-marangoni problem in an annular domain with temperature gradient |
publisher |
VINCA Institute of Nuclear Sciences |
series |
Thermal Science |
issn |
0354-9836 2334-7163 |
publishDate |
2017-01-01 |
description |
This manuscript addresses the linear stability analysis of a thermoconvective problem in an annular domain. The flow is heated from below, with a linear decreasing horizontal temperature profile from the inner to the outer wall. The top surface of the domain is open to the atmosphere and the two lateral walls are adiabatic. The effects of several parameters in the flow are evaluated. Three different values for the ratio of the momentum diffusivity and thermal diffusivity are considered: relatively low Prandtl number (Pr = 1), intermediate Prandtl number (Pr = 5) and high Prandtl number (ideally Pr → ∞ , namely Pr = 50). The thermal boundary condition on the top surface is changed by imposing different values of the Biot number, Bi. The influence of the aspect ratio (Γ) is assessed for through by studying several aspect ratios, Γ. The study has been performed for two values of the Bond number (namely Bo = 5 and 50), estimating the perturbation given by thermocapillarity effects on buoyancy effects. Different kinds of competing solutions appear on localized zones of the Γ-Bi plane. The boundaries of these zones are made up of co-dimension two points. Co-dimension two points are found to be function of Bond number, Marangoni number and boundary conditions but to be independent on the Prandtl number. |
topic |
Marangoni problem Thermocapillary convection Linear stability Buoyancy Effects |
url |
http://www.doiserbia.nb.rs/img/doi/0354-9836/2017/0354-98361600277H.pdf |
work_keys_str_mv |
AT hoyassergio ontheonsetofinstabilitiesinabenardmarangoniprobleminanannulardomainwithtemperaturegradient AT ianiroandrea ontheonsetofinstabilitiesinabenardmarangoniprobleminanannulardomainwithtemperaturegradient AT perezquilesmariaj ontheonsetofinstabilitiesinabenardmarangoniprobleminanannulardomainwithtemperaturegradient AT fajardopablo ontheonsetofinstabilitiesinabenardmarangoniprobleminanannulardomainwithtemperaturegradient |
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