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The Axisymmetric Laminar Plume: Asymptotic Solution for Large Prandtl Number

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The method of matched asymptotic expansions is applied to the axisymmetric boundary‐layer equations in order to determine approximate solutions for free convection from a point source of buoyancy in the limit of large Prandtl number (σ ≫ 1). In common with other types of free‐convection boundary layers at large Prandtl number, there is an inner region in which the temperature decays to its far‐field value, and a much wider, outer region in which the vorticity decays to zero. Unlike the other cases, the velocity is not of the same order of magnitude in the two regions, but is larger in the inner region by a factor of order 1n(1/∈2) in the inner region, where ∈ is a root of ∈41n(1/∈2)=1/σ.
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Document Type: Research Article

Affiliations: Massachusetts Institute of Technology

Publication date: October 1, 1986

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