Bifurcation Diversity in an Annular Pool Heated from Below: Prandtl and Biot Numbers Effects
A. J. Torregrosa 1, S. Hoyas 1*, M. J. Perez-Quiles 2, J. M. Mompo-Laborda 11 CMT-Motores Termicos, Universitat Politecnica de Valencia, Valencia 46022, Spain.
2 Instituto Universitario de Matematica Pura y Aplicada, Universitat Politecnica de Valencia, Valencia 46022, Spain.
Received 9 June 2011; Accepted (in revised version) 17 February 2012
Available online 28 June 2012
In this article the instabilities appearing in a liquid layer are studied numerically by means of the linear stability method. The fluid is confined in an annular pool and is heated from below with a linear decreasing temperature profile from the inner to the outer wall. The top surface is open to the atmosphere and both lateral walls are adiabatic. Using the Rayleigh number as the only control parameter, many kind of bifurcations appear at moderately low Prandtl numbers and depending on the Biot number. Several regions on the Prandtl-Biot plane are identified, their boundaries being formed from competing solutions at codimension-two bifurcation points.AMS subject classifications: 76R10, 35P15
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Key words: Thermocapillary convection, Prandtl number, Biot number, linear stability.
Email: email@example.com (A. J. Torregrosa), firstname.lastname@example.org (S. Hoyas), email@example.com (M. J. Perez-Quiles), firstname.lastname@example.org (J. M. Mompo-Laborda)