Thermal Convection for Large Prandtl Numbers

Siegfried Grossmann; Detlef Lohse

doi:10.1103/PhysRevLett.86.3316

Thermal Convection for Large Prandtl Numbers

Siegfried Grossmann and Detlef Lohse

Phys. Rev. Lett. 86, 3316 – Published 9 April 2001

Abstract

The Rayleigh-Bénard 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 a maximum in the Nu(Pr) dependence is predicted. We moreover offer the full functional dependences of Nu(Ra,Pr) and Re(Ra,Pr) within this extended theory, rather than only give the limiting power laws as done in J. Fluid. Mech. 407, 27 (2000). This enables us to more realistically describe the transitions between the various scaling regimes.

Received 26 July 2000

DOI:https://doi.org/10.1103/PhysRevLett.86.3316

Authors & Affiliations

Siegfried Grossmann¹ and Detlef Lohse²

¹Department of Physics, University of Marburg, Renthof 6, D-35032 Marburg, Germany
²Department of Applied Physics and J. M. Burgers Centre for Fluid Dynamics, University of Twente, 7500 AE Enschede, The Netherlands