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Effect of a non-uniform basic temperature gradient on the onset of Bénard-Marangoni convection: Stationary and oscillatory analyses

✍ Scribed by Ko-Ta Chiang

Publisher
Elsevier Science
Year
2005
Tongue
English
Weight
299 KB
Volume
32
Category
Article
ISSN
0735-1933

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✦ Synopsis

The qualitative effect of a non-uniform basic temperature gradient on the stationary and oscillatory stability analyses of the onset of Be ´nard-Marangoni convective in a horizontal fluid layer is investigated numerically using the fourth order Runger-Kutta-Gill's method coupled with the iterative Broyden's method. The effects of crispation at a deformable upper free surface and the conductive effect of non-steady conditions within the fluid layer on onset are discussed. Results show that the effect of crispation (i.e., Crispation number C) is a clearly destabilizing factor, but the conductive effect (i.e., a i * of non-steady conditions within the fluid layer does play a stabilizing state. The system becomes more stable at larger values of the Prandtl number Pr, the Biot number B i and the Bond number B o . We obtain a set of characteristic curves in the (M C , R)-plane that satisfy the linear relation on the onset of the stationary and oscillatory Be ´nard-Marangoni convective instability.

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