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A spectral method determination of the first critical Rayleigh number for a low-Prandtl number crystal melt in a cylindrical container

Author
Dietz, C. M., Jr.
Published
Jul 1, 1993.
Physical Description
1 electronic document
Additional Creators
Diplas, P.
Online Version

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Summary
The onset of laminar axisymmetric Rayleigh-Benard convection is investigated for a low-Prandtl number liquid metal in a cylindrical container. All surfaces are considered to be solid and no-slip. Two separate cases are examined for the thermal boundary conditions at the side wall, one with conducting and the other with insulated surface. The governing Boussinesq system is first perturbed and then simplified by introducing a Stokes stream function. Subsequently, a Chebyshev Galerkin spectral model is employed to reduce the simplified system to a system of first-order nonlinear ordinary differential equations. A local stability analysis determines the two values of the first critical Rayleigh number, Ra(sub cl), for the insulated and conducting side walls. As expected, the conducting Ra(sub cl) value of 2882.5 obtained from the present approach exceeded the corresponding insulated Ra(sub cl) value of 2331.6. For the insulated case, an earlier study using a different numerical approach suggests that Ra(sub cl) = 2261.9, while an experimental study measured Ra(sub cl) = 2700.
Other Subject(s)
Collection
NASA Technical Reports Server (NTRS) Collection.
Note
Document ID: 19930020025.
Accession ID: 93N29214.
NASA-CR-193238.
NAS 1.26:193238.
Terms of Use and Reproduction
No Copyright.
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