2000/11/08 by Siegfried Grossmann, Siegfried Großmann, Detlef Lohse · 5 citations
Chemical Engineering · Engineering · Mathematics · Physics and Astronomy · #Convection #Fluid Dynamics and Turbulent Flows #Geometry #Limiting #Mathematics #Natural convection #Nusselt number #Phase Equilibria and Thermodynamics #Physics #Prandtl number #Rayleigh number #Reynolds number #Rheology and Fluid Dynamics Studies #Scaling #Thermodynamics #Turbulence #nlin.CD
paper · pdf · doi:10.1103/physrevlett.86.3316
published as Phys. Rev. Lett. 86, 3316-3319 (2001) · 7 pages
arxiv created 2000/11/08 · openalex publication_date 2001/04/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.