Thermal convection for large Prandtl numbers

Siegfried Grossmann; Detlef Lohse

doi:10.1103/PhysRevLett.86.3316

Thermal convection for large Prandtl numbers

Siegfried Grossmann, Detlef Lohse

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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.

Original language	Undefined
Pages (from-to)	3316-3319
Number of pages	4
Journal	Physical review letters
Volume	86
Issue number	15
DOIs	https://doi.org/10.1103/PhysRevLett.86.3316
Publication status	Published - 2001

Keywords

METIS-202009
IR-36431

Access to Document

10.1103/PhysRevLett.86.3316

thermal_convection

Cite this

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title = "Thermal convection for large Prandtl numbers",

abstract = "The Rayleigh-B{\'e}nard 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.",

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T1 - Thermal convection for large Prandtl numbers

AU - Grossmann, Siegfried

AU - Lohse, Detlef

PY - 2001

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N2 - 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.

AB - 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.

KW - METIS-202009

KW - IR-36431

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