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Thermal convection in an inclined porous layer with Brinkman law

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Abstract

A model for thermal convection of a fluid saturating an inclined layer of porous medium with a Brinkman law and stress-free boundary conditions is studied. When the Darcy number \(\tilde{D}a\) is zero, this problem has been studied by Rees and Bassom (Acta Mech 144(1–2):103–118, 2000). When the Brinkman term is present in the model (\(\tilde{D}a\not =0\)) the basic motion is a combination of hyperbolic and polynomial functions. With the Chebyshev collocation method we study the linear instability of the basic motion for three-dimensional perturbations. We also give nonlinear stability conditions and, for longitudinal perturbations, we prove the coincidence of linear and nonlinear critical Rayleigh numbers.

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Acknowledgements

Research partially supported by the University of Catania under the contract “Analisi qualitativa per sistemi dinamici finito e infinito dimensionali con applicazioni a biomatematica, meccanica dei continui e termodinamica estesa classica e quantistica” and by “Gruppo Nazionale della Fisica Matematica” of the “Istituto Nazionale di Alta Matematica”. We thank Brian Straughan for helpful discussions on this subject. The authors acknowledge support from the project PON SCN 00451 CLARA - CLoud plAtform and smart underground imaging for natural Risk Assessment, Smart Cities and Communities and Social Innovation.

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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Città Universitaria, Viale A. Doria, 6, 95125, Catania, Italy

    Paolo Falsaperla & Giuseppe Mulone

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  1. Paolo Falsaperla
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  2. Giuseppe Mulone
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Correspondence to Paolo Falsaperla.

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This paper is dedicated to Prof. Tommaso Ruggeri in the occasion of his 70th birthday.

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Falsaperla, P., Mulone, G. Thermal convection in an inclined porous layer with Brinkman law. Ricerche mat 67, 983–999 (2018). https://doi.org/10.1007/s11587-018-0371-2

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  • DOI: https://doi.org/10.1007/s11587-018-0371-2

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