An asymptotic solution for slightly buoyant laminar plumes

P. Wesseling

    Research output: Contribution to journalArticleAcademic

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    Abstract

    When the buoyancy forces are small compared with the inertia forces, heated plumes in laminar flows which are uniform at upstream infinity approximately satisfy a linearized version of the Boussinesq equations, here called the Oseen–Boussinesq equations. An analytic solution is constructed for arbitrary Prandtl number and arbitrary direction of the unperturbed flow in the case of a plume produced by a point source. The two-dimensional case of the plume from a line source is considered briefly. A Stokes-type paradox occurs: it is found that a line-source solution that vanishes at infinity does not exist.
    Original languageEnglish
    Pages (from-to)81-87
    JournalJournal of fluid mechanics
    Volume70
    Issue number1
    DOIs
    Publication statusPublished - 1975

    Fingerprint

    Prandtl number
    Buoyancy
    Laminar flow
    plumes
    infinity
    paradoxes
    laminar flow
    buoyancy
    inertia
    upstream
    point sources

    Cite this

    Wesseling, P. / An asymptotic solution for slightly buoyant laminar plumes. In: Journal of fluid mechanics. 1975 ; Vol. 70, No. 1. pp. 81-87.
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    author = "P. Wesseling",
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    language = "English",
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    An asymptotic solution for slightly buoyant laminar plumes. / Wesseling, P.

    In: Journal of fluid mechanics, Vol. 70, No. 1, 1975, p. 81-87.

    Research output: Contribution to journalArticleAcademic

    TY - JOUR

    T1 - An asymptotic solution for slightly buoyant laminar plumes

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    PY - 1975

    Y1 - 1975

    N2 - When the buoyancy forces are small compared with the inertia forces, heated plumes in laminar flows which are uniform at upstream infinity approximately satisfy a linearized version of the Boussinesq equations, here called the Oseen–Boussinesq equations. An analytic solution is constructed for arbitrary Prandtl number and arbitrary direction of the unperturbed flow in the case of a plume produced by a point source. The two-dimensional case of the plume from a line source is considered briefly. A Stokes-type paradox occurs: it is found that a line-source solution that vanishes at infinity does not exist.

    AB - When the buoyancy forces are small compared with the inertia forces, heated plumes in laminar flows which are uniform at upstream infinity approximately satisfy a linearized version of the Boussinesq equations, here called the Oseen–Boussinesq equations. An analytic solution is constructed for arbitrary Prandtl number and arbitrary direction of the unperturbed flow in the case of a plume produced by a point source. The two-dimensional case of the plume from a line source is considered briefly. A Stokes-type paradox occurs: it is found that a line-source solution that vanishes at infinity does not exist.

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    DO - 10.1017/S0022112075001905

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    JF - Journal of fluid mechanics

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