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Old Problems Revisited from New Perspectives in Implicit Theories of Fluids

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Non-Newtonian Fluid Mechanics and Complex Flows

Part of the book series: Lecture Notes in Mathematics ((LNMCIME,volume 2212))

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Abstract

Three of the most studied problems in fluid dynamics are revisited within implicit theories of fluids. Specifically, the onset of convection, the determination of laminar flows and the motion of a fluid down an inclined plane are studied under the assumption that the Cauchy stress tensor and the rate-of-strain tensor are related through implicit constitutive equations. Particular attention is paid to fluids whose viscosities are pressure-dependent.

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Notes

  1. 1.

    For the sake of self-consistency, if Σ is a smooth scalar, vector or tensor field defined on the trajectory of the body \(\mathcal {B}\), \(\dot {\varSigma }=\varSigma _t+(\boldsymbol {v}\cdot \nabla )\varSigma \).

  2. 2.

    The other physical properties measured by Bridgman are the isothermal compressibility, the thermal expansion coefficient, the specific heat and the thermal conductivity.

  3. 3.

    Assuming that Ω is a horizontal layer is convenient for deriving the set of approximations we shall adopt in this paper. However, the analysis we are going to perform can be adapted, by means of slight changes, to the case in which Ω is bounded in one direction provided that such a direction is non-horizontal.

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Authors and Affiliations

  1. Dipartimento di Ingegneria, Università degli Studi di Perugia, Perugia, Italy

    Giuseppe Saccomandi

  2. School of Mathematics, Statistics and Applied Mathematics, National University of Ireland Galway, Galway, Ireland

    Giuseppe Saccomandi

  3. Dipartimento di Ingegneria, Università degli Studi di Perugia, Perugia, Italy

    Luigi Vergori

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  1. Giuseppe Saccomandi
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  2. Luigi Vergori
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Correspondence to Giuseppe Saccomandi .

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Editors and Affiliations

  1. Dipartimento di Matematica e Informatica "Ulisse Dini", Università degli Studi di Firenze , Firenze, Italy

    Angiolo Farina

  2. Département de Mathématiques, Institut Camille Jordan, Université Claude Bernard Lyon 1, Villeurbanne, France

    Andro Mikelić

  3. Dipartimento di Matematica e Informatica "Ulisse Dini", Università degli Studi di Firenze, Firenze, Italy

    Fabio Rosso

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Saccomandi, G., Vergori, L. (2018). Old Problems Revisited from New Perspectives in Implicit Theories of Fluids. In: Farina, A., Mikelić, A., Rosso, F. (eds) Non-Newtonian Fluid Mechanics and Complex Flows. Lecture Notes in Mathematics(), vol 2212. Springer, Cham. https://doi.org/10.1007/978-3-319-74796-5_2

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