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Whittaker, Robert J. 
ORCID: https://orcid.org/0000-0001-9598-5938 and Lister, John R.
(2006)
Steady axisymmetric creeping plumes above a planar boundary. Part 2. A distributed source.
Journal of Fluid Mechanics, 567.
pp. 379-397.
ISSN 0022-1120
Abstract
Asymptotic solutions are obtained for an axisymmetric plume rising from a localized heat source at the base of a half-space filled with very viscous fluid. Specifically, we consider sources comprising a heated disk with either rigid (no-slip) or free-slip (no tangential stress) conditions on the lower boundary. The boundary layer which forms above the source is solved using stretched coordinates, and then matched to a slender plume which rises above it. At large Rayleigh numbers, the Nusselt number is given by $Nu \sim 4.06 Ra^{1/3}(\ln Ra)^{-1/3}$ (free-slip boundary) and $Nu \sim 2.90 Ra^{1/5}$ (rigid boundary), where the Rayleigh number is based on the radius of the source. Both these expressions have corrections arising from a slender-body expansion in powers of $(\ln Ra)^{-1}$.
| Item Type: | Article |
|---|---|
| Faculty \ School: | Faculty of Science > School of Mathematics |
| UEA Research Groups: | Faculty of Science > Research Groups > Fluid and Solid Mechanics |
| Depositing User: | Robert Whittaker |
| Date Deposited: | 10 Mar 2011 12:48 |
| Last Modified: | 24 Oct 2022 02:05 |
| URI: | https://ueaeprints.uea.ac.uk/id/eprint/20894 |
| DOI: | 10.1017/S0022112006002382 |
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