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  • Similarity Solutions of Radially Symmetric Two-Phase Flow

    Author(s)
    Weeks, Scott
    Sander, G.
    Lisle, I.
    Parlange, J.
    Griffith University Author(s)
    Weeks, Scott W.
    Year published
    1994
    Metadata
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    Abstract
    When both the diffusivityD and fractional flow functionf have a power law dependence on the water content θ, i.e.D=Doθα andf=θα+1, the nonlinear transport equation for radially symmetric two phase flow can, in certain circumstances, be reduced to a weakly coupled system of two first order nonlinear ordinary differential equations. Numerical solutions of these equations for a constant flux boundary conditionVwo and comparison with experimental data are given. In particular, when the fluxVwo and a are related byVwo(α + 1)/Do=2, a new fully explicit analytical solution is found as θ(r, t)=(1 − αr2/4Dot)1/α forr2 < 4Dot/α and ...
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    When both the diffusivityD and fractional flow functionf have a power law dependence on the water content θ, i.e.D=Doθα andf=θα+1, the nonlinear transport equation for radially symmetric two phase flow can, in certain circumstances, be reduced to a weakly coupled system of two first order nonlinear ordinary differential equations. Numerical solutions of these equations for a constant flux boundary conditionVwo and comparison with experimental data are given. In particular, when the fluxVwo and a are related byVwo(α + 1)/Do=2, a new fully explicit analytical solution is found as θ(r, t)=(1 − αr2/4Dot)1/α forr2 < 4Dot/α and θ(r, t)=0 forr2 ≥ 4Dot/α We show that the existence of this exact soution is due to the presence of a Lagrangian symmetry.
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    Journal Title
    Journal of Applied Mathematics and Physics
    Volume
    45
    Issue
    6
    Publisher URI
    https://link.springer.com/article/10.1007/BF00952080
    Subject
    Mathematical Sciences
    Applied Mathematics
    Mathematical Physics
    Publication URI
    http://hdl.handle.net/10072/119666
    Collection
    • Journal articles

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