A finite element model for magnetohydrodynamic squeeze-film flows

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dc.citation.articleNumber123103en_US
dc.citation.issueNumber12en_US
dc.citation.journalTitlePhysics of Fluidsen_US
dc.citation.volumeNumber30en_US
dc.contributor.authorWagner, Jordan R.en_US
dc.contributor.authorHiggs, C. Fred IIIen_US
dc.date.accessioned2019-01-18T17:51:32Zen_US
dc.date.available2019-01-18T17:51:32Zen_US
dc.date.issued2018en_US
dc.description.abstractA computational model is developed to analyze magnetohydrodynamic (MHD) squeeze-film flows featuring an electrically conducting fluid subjected to imposed magnetic and electric fields. The model is based on the so-called MHD Reynolds equation for squeeze-films—an extension of the classical hydrodynamic Reynolds equation. A complete derivation of the MHD Reynolds equation is performed by applying thin-film and quasi-steady assumptions to the Maxwell/Navier-Stokes system coupled by the Lorentz force. The resulting equation is a two-dimensional and variable-coefficient Poisson equation for pressure, which reduces to the purely hydrodynamic form in the limit of vanishing Hartmann number. A geometric calculus formulation facilitates the reduction of the mathematical system into two dimensions, which is a challenge in standard vector calculus due to the cross product. The model permits realistic geometrical representations of the constraining squeeze-surfaces, and we demonstrate the use of a multi-variate Weierstrass-Mandelbrot fractal to numerically generate scale-invariant surface roughness profiles. Ultimately, the governing equation is solved with the Galerkin finite element method. Several numerical examples are conducted to highlight some of the model’s capabilities. MHD forces—as well as the roughness, geometry, and topology of the squeeze surfaces—are shown to significantly influence flow characteristics.en_US
dc.identifier.citationWagner, Jordan R. and Higgs, C. Fred III. "A finite element model for magnetohydrodynamic squeeze-film flows." <i>Physics of Fluids,</i> 30, no. 12 (2018) AIP Publishing LLC: https://doi.org/10.1063/1.5064598.en_US
dc.identifier.doihttps://doi.org/10.1063/1.5064598en_US
dc.identifier.urihttps://hdl.handle.net/1911/105115en_US
dc.language.isoengen_US
dc.publisherAIP Publishing LLCen_US
dc.rightsArticle is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.en_US
dc.titleA finite element model for magnetohydrodynamic squeeze-film flowsen_US
dc.typeJournal articleen_US
dc.type.dcmiTexten_US
dc.type.publicationpublisher versionen_US
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