Convection in a horizontally heated sphere
Natural convection in horizontally heated spherical fluid-filled cavities is considered in the low Grashof number limit. The equations governing the asymptotic expansion are derived for all orders. At each order a Stokes problem must be solved for the momentum correction. The general solution of the...
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Published in | Journal of fluid mechanics Vol. 438; pp. 1 - 10 |
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Main Author | |
Format | Journal Article |
Language | English |
Published |
Cambridge, UK
Cambridge University Press
10.07.2001
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Subjects | |
Online Access | Get full text |
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Summary: | Natural convection in horizontally heated spherical fluid-filled cavities is considered in
the low Grashof number limit. The equations governing the asymptotic expansion are
derived for all orders. At each order a Stokes problem must be solved for the momentum
correction. The general solution of the Stokes problem in a sphere with arbitrary
smooth body force is derived and used to obtain the zeroth-order (creeping) flow and
the first-order corrections due to inertia and buoyancy. The solutions illustrate the two
mechanisms adduced by Mallinson & de Vahl Davis (1973, 1977) for spanwise flow in
horizontally heated cuboids. Further, the analytical derivations and expressions clarify
these mechanisms and the conditions under which they do not operate. The inertia
and buoyancy effects vanish with the Grashof and Rayleigh numbers, respectively,
and both vanish if the flow is purely vertical, as in a very tall and narrow cuboid. |
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Bibliography: | istex:A1E8441C407E43B05DE632948EC882202BC212D4 PII:S0022112001003913 ark:/67375/6GQ-GZMTMKFL-5 |
ISSN: | 0022-1120 1469-7645 |
DOI: | 10.1017/S0022112001003913 |