THERMAL SCIENCE

International Scientific Journal

Sergio Hoyas

,

Andrea Ianiro

,

María J. Perez-Quiles

,

Pablo Fajardo

ON THE ONSET OF INSTABILITIES IN A BéNARD-MARANGONI PROBLEM IN AN ANNULAR DOMAIN WITH TEMPERATURE GRADIENT

ABSTRACT
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.
KEYWORDS
Marangoni problem, Thermocapillary convection, linear stability, Buoyancy Effects
PAPER SUBMITTED: 2016-06-28
PAPER REVISED: 2016-09-06
PAPER ACCEPTED: 2016-09-06
PUBLISHED ONLINE: 2016-11-06
DOI REFERENCE: https://doi.org/10.2298/TSCI160628277H
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2017, VOLUME 21, ISSUE Supplement 3, PAGES [S585 - S596]
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On the onset of instabilities in a Bénard-Marangoni problem in an annular domain with temperature gradient

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