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Weakly nonlinear viscoplastic convection

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Title: Weakly nonlinear viscoplastic convection
Authors: Balmforth, Neil J.1,2, Rust, Alison C.3 Alison.Rust@bristol.ac.uk
Source: Journal of Non-Newtonian Fluid Mechanics. May2009, Vol. 158 Issue 1-3, p36-45. 10p.
Subjects: Heat convection, Viscoplasticity, Viscous flow, Rayleigh number, Newtonian fluids, Shear (Mechanics), Viscosity
Abstract: Abstract: The development of thermal convection is studied for a viscoplastic fluid. If the viscosity is finite at zero shear rate, the critical Rayleigh number for linear instability takes the value given by a Newtonian fluid with that viscosity. The subsequent weakly nonlinear behaviour depends on the degree of shear thinning: with moderate shear thinning, convective overturning for a given temperature difference is amplified relative to the Newtonian case. If the reduction in viscosity is sufficiently sharp the transition becomes subcritical (the relevant situation for many regularized constitutive laws). For an infinite viscosity at zero shear rate, or a yield-stress, the critical Rayleigh number for linear instability is infinite. Nonlinear convective overturning, however, is still possible; we trace out how the finite-amplitude solution branches develop from their Newtonian counterparts as the yield stress is increased from zero for the Bingham fluid. Laboratory experiments with a layer of Carbopol fluid heated from below confirm that yield strength inhibits convection but a sufficiently strong perturbation can initiate overturning. [Copyright &y& Elsevier]
Copyright of Journal of Non-Newtonian Fluid Mechanics is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
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PubType: Academic Journal
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PreciseRelevancyScore: 0
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  Data: <searchLink fieldCode="DE" term="%22Heat+convection%22">Heat convection</searchLink><br /><searchLink fieldCode="DE" term="%22Viscoplasticity%22">Viscoplasticity</searchLink><br /><searchLink fieldCode="DE" term="%22Viscous+flow%22">Viscous flow</searchLink><br /><searchLink fieldCode="DE" term="%22Rayleigh+number%22">Rayleigh number</searchLink><br /><searchLink fieldCode="DE" term="%22Newtonian+fluids%22">Newtonian fluids</searchLink><br /><searchLink fieldCode="DE" term="%22Shear+%28Mechanics%29%22">Shear (Mechanics)</searchLink><br /><searchLink fieldCode="DE" term="%22Viscosity%22">Viscosity</searchLink>
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  Data: Abstract: The development of thermal convection is studied for a viscoplastic fluid. If the viscosity is finite at zero shear rate, the critical Rayleigh number for linear instability takes the value given by a Newtonian fluid with that viscosity. The subsequent weakly nonlinear behaviour depends on the degree of shear thinning: with moderate shear thinning, convective overturning for a given temperature difference is amplified relative to the Newtonian case. If the reduction in viscosity is sufficiently sharp the transition becomes subcritical (the relevant situation for many regularized constitutive laws). For an infinite viscosity at zero shear rate, or a yield-stress, the critical Rayleigh number for linear instability is infinite. Nonlinear convective overturning, however, is still possible; we trace out how the finite-amplitude solution branches develop from their Newtonian counterparts as the yield stress is increased from zero for the Bingham fluid. Laboratory experiments with a layer of Carbopol fluid heated from below confirm that yield strength inhibits convection but a sufficiently strong perturbation can initiate overturning. [Copyright &y& Elsevier]
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  Group: Ab
  Data: <i>Copyright of Journal of Non-Newtonian Fluid Mechanics is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1016/j.jnnfm.2008.07.012
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      – Code: eng
        Text: English
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        PageCount: 10
        StartPage: 36
    Subjects:
      – SubjectFull: Heat convection
        Type: general
      – SubjectFull: Viscoplasticity
        Type: general
      – SubjectFull: Viscous flow
        Type: general
      – SubjectFull: Rayleigh number
        Type: general
      – SubjectFull: Newtonian fluids
        Type: general
      – SubjectFull: Shear (Mechanics)
        Type: general
      – SubjectFull: Viscosity
        Type: general
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      – TitleFull: Weakly nonlinear viscoplastic convection
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              Text: May2009
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              Y: 2009
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