Thermocapillary Driven Turbulent Heat Transfer

[+] Author and Article Information
V. S. Arpacı, S.-H. Kao

Department of Mechanical Engineering and Applied Mechanics, The University of Michigan, 2142 G. G. Brown, 2350 Hayward, Ann Arbor, MI 48109-2125

J. Heat Transfer 120(1), 214-219 (Feb 01, 1998) (6 pages) doi:10.1115/1.2830044 History: Received August 21, 1996; Revised August 22, 1997; Online January 07, 2008


A dimensionless number depending on the usual Prandtl and Marangoni numbers, Πs ∼ Ma/(1 + Pr1 ) = Ma Pr/(1 + Pr), is introduced for thermocapillary driven flows. Three heat transfer models are proposed in terms of Πs . The first model on laminar flow, using some dimensional arguments with a flow scale and the boundary layer concept, leads to Nu ∼ Πs1/4, Nu being the usual Nusselt number. The second model on transition flow, extending Landau’s original idea on the amplitude of disturbances past marginal stability of isothermal flow, leads to Nu − 1 ∼ (ΠS −ΠS c )1/2 , ΠS c corresponding to the critical value of Πs for the marginal state. The third model on turbulent flow, introduces a thermal microscale ηθ ∼ (1 + Pr-1 )1/4 (να2 /P s )1/4 = (1 + Pr)1/4 (α3 /P s )1/4 , with ν and α, respectively, being kinematic and thermal diffusivities, and P s the production rate of thermocapillary energy. The first expression relating ηθ to Prandtl number explicitly includes its limit for Pr → ∞, ηθB ∼ (να2 /ε)1/4 , which is a Batchelor scale, and the second one explicitly includes its limit for Pr → 0, ηθC ∼ (α3 /ε)1/4 , which is an Oboukhov-Corrsin scale. In terms of ηθ and an integral scale l, the model leads to Nu ∼ l/ηθ ∼ Πs1/3. Recent experimental literature are interpreted by special cases of the foregoing models corresponding to Pr > 1.

Copyright © 1998 by The American Society of Mechanical Engineers
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