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Heat-flow experiments in liquid 4He with a variable cylindrical geometry

Published online by Cambridge University Press:  21 April 2006

H. Gao,
G. Metcalfe,
T. Jung and
R. P. Behringer
H. Gao
Affiliation:
Duke University, Durham, NC 27706, USA
G. Metcalfe
Affiliation:
Duke University, Durham, NC 27706, USAPresent address: Department of Physics, University of Maryland, College Park, MD 20742, USA.
T. Jung
Affiliation:
Duke University, Durham, NC 27706, USA
R. P. Behringer
Affiliation:
Duke University, Durham, NC 27706, USA
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Abstract

This paper first describes an apparatus for measuring the Nusselt number N versus the Rayleigh number R of convecting normal liquid 4He layers. The most important feature of the apparatus is its ability to provide layers of different heights d, and hence different aspect ratios [Gcy ]. The horizontal cross-section of each layer is circular, and [Gcy ] is defined by [Gcy ] = D/2d where D is the diameter of the layer. We report results for 2.4 [les ] [Gcy ] [les ] 16 and for Prandtl numbers Pr spanning 0.5 [lsim] Pr [lsim] 0.9 These results are presented in terms of the slope N1 = RcdN/dR evaluated just above the onset of convection at Rc. We find that N1 is only a slowly increasing function of [Gcy ] in the range 6 [lsim] [Gcy ] [lsim] 16, and that it has a value there which is quite close to 0.72. This value of N1 is in good agreement with variational calcuations by Ahlers et al. (1981) pertinent to parallel convection rolls in cylindrical geometry. Particularly for [Gcy ] [lsim] 6, we find additional small-scale structure in N1 associated with changes in the number of convection rolls with changing [Gcy ]. An additional test of the linearzied hydrodynamics is given by measurements of Rc. We find good agreement between theory and our data for Rc.

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Type
Research Article
Information
Journal of Fluid Mechanics , Volume 174 , January 1987, pp. 209 - 231
Copyright
© 1987 Cambridge University Press

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