# Steady axisymmetric creeping plumes above a planar boundary. Part 2. A distributed source

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

Full text not available from this repository. (Request a copy)

## 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 of Science > School of Mathematics Robert Whittaker 10 Mar 2011 12:48 24 Oct 2022 02:05 https://ueaeprints.uea.ac.uk/id/eprint/20894 10.1017/S0022112006002382