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Pattern selection in the thermal convection of non-Newtonian fluids

Published online by Cambridge University Press:  05 January 2011

BASHAR ALBAALBAKI  and
ROGER E. KHAYAT
BASHAR ALBAALBAKI
Affiliation:
Department of Mechanical and Materials Engineering, The University of Western Ontario, London, Ontario N6A 5B9, Canada
ROGER E. KHAYAT*
Affiliation:
Department of Mechanical and Materials Engineering, The University of Western Ontario, London, Ontario N6A 5B9, Canada
*
†Email address for correspondence: [email protected]
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Abstract

The thermogravitational instability in a fluid layer of a non-Newtonian medium heated from below is investigated. Linear and weakly nonlinear analyses are successively presented. The fluid is assumed to obey the Carreau–Bird model. Although the critical threshold is the same as for a Newtonian fluid, it is found that non-Newtonian fluids can convect in the form of rolls, squares or hexagons, depending on the shear-thinning level. Similar to Newtonian fluids, shear-thickening fluids convect only in the form of rolls. The stability of the convective steady branches is carried out to determine under which specific conditions a pattern is preferred. The influence of the rheological and physical parameters is examined and discussed in detail.

JFM classification

Non-Newtonian Flows: Non-Newtonian Flows Nonlinear Dynamical Systems: Pattern formation
Type
Papers
Information
Journal of Fluid Mechanics , Volume 668 , 10 February 2011 , pp. 500 - 550
Copyright
Copyright © Cambridge University Press 2011

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References

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