Thermal convection for large Prandtl numbers

Details Thermal convection for large Prandtl numbers Thermal convection for large Prandtl numbers

2000-11-08

arxiv.org/abs/nlin/0011015v1

Phys. Rev. Lett. 86, 3316-3319 (2001)

Nonlinear Sciences

Chaotic Dynamics

7 pages

Scientific paper

10.1103/PhysRevLett.86.3316

The Rayleigh-Benard theory by Grossmann and Lohse [J. Fluid Mech. 407, 27 (2000)] is extended towards very large Prandtl numbers Pr. The Nusselt number Nu is found here to be independent of Pr. However, for fixed Rayleigh numbers Ra> 10^{10} a maximum around Pr= 2 in the Nu(Pr)-dependence is predicted which is absent for lower Ra. We moreover offer the full functional dependences of Nu(Ra,Pr) and Re(Ra,Pr) within this extended theory, rather than only giving the limiting power laws as done previously. This enables us to more realistically describe the transitions between the various scaling regimes, including their widths.

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