Stability of penetrative convective currents in local thermal non-equilibrium

Giuseppe Arnone; Florinda Capone; Jacopo Alfonso Gianfrani

doi:10.1098/rspa.2023.0820

Stability of penetrative convective currents in local thermal non-equilibrium

Giuseppe Arnone, Florinda Capone, Jacopo Alfonso Gianfrani

Research Centre for Fluid and Complex Systems

Federico II University

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

114 Downloads (Pure)

Abstract

The aim of this paper is to investigate the onset of penetrative convection in a Darcy–Brinkman porous medium under the hypothesis of local thermal non-equilibrium. For the problem at stake, the strong form of the principle of exchange of stabilities has been proved, i.e. convective motions can occur only through secondary stationary motions. We perform linear and nonlinear stability analyses of the basic state, with particular regard to the behaviour of stability thresholds with respect to the relevant physical parameters characterizing the problem. The Chebyshev- τ method and the shooting method are employed and accurately implemented to solve the differential eigenvalue problems arising from linear and nonlinear analyses to determine critical Rayleigh numbers. Via numerical simulations, the stabilizing effect of the upper bounding plane temperature, of the Darcy number and of the interaction coefficient for the heat exchange, is demonstrated.

Original language	English
Article number	20230820
Journal	Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume	480
Issue number	2287
Early online date	10 Apr 2024
DOIs	https://doi.org/10.1098/rspa.2023.0820
Publication status	E-pub ahead of print - 10 Apr 2024

Bibliographical note

© 2024 The Author(s) Published by the Royal Society. All rights reserved
Copyright © and Moral Rights are retained by the author(s) and/ or other copyright owners. A copy can be downloaded for personal non-commercial research or study, without prior permission or charge. This item cannot be reproduced or quoted extensively from without first obtaining permission in writing from the copyright holder(s). The content must not be changed in any way or sold commercially in any format or medium without the formal permission of the copyright holders.

This document is the author’s post-print version, incorporating any revisions agreed during the peer-review process. Some differences between the published version and this version may remain and you are advised to consult the published version if you wish to cite from it.

Funder

This paper has been performed under the auspices of the GNFM of INdAM. The authors would like to thank the anonymous reviewers for the precious comments that led to the improvement of the manuscript. The authors acknowledge the support of National Recovery and Resilience Plan (NRRP) funded by the European Union - NextGenerationEU - Project Title \u201CMathematical Modeling of Biodiversity in the Mediterranean sea: from bacteria to predators, from meadows to currents\u201D - project code P202254HT8 (CUP B53D23027760001) and the support of grant no. MUR-PRIN PNNR 2022 - Project Title \u201CModelling complex biOlogical systeMs for biofuEl productioN and sTorAge: mathematics meets green industry\u201D - project code 202248TY47 (CUP E53D23005430006).

Funding

This paper has been performed under the auspices of the GNFM of INdAM. The authors would like to thank the anonymous reviewers for the precious comments that led to the improvement of the manuscript. The authors acknowledge the support of National Recovery and Resilience Plan (NRRP) funded by the European Union - NextGenerationEU - Project Title \u201CMathematical Modeling of Biodiversity in the Mediterranean sea: from bacteria to predators, from meadows to currents\u201D - project code P202254HT8 (CUP B53D23027760001) and the support of grant no. MUR-PRIN PNNR 2022 - Project Title \u201CModelling complex biOlogical systeMs for biofuEl productioN and sTorAge: mathematics meets green industry\u201D - project code 202248TY47 (CUP E53D23005430006).

Funders	Funder number
European Union
Istituto Nazionale di Alta Matematica "Francesco Severi"
Gruppo Nazionale per la Fisica Matematica
European Commission	CUP E53D23005430006, CUP B53D23027760001, MUR-PRIN PNNR 2022, 202248TY47

Keywords

density inversion
local thermal non-equilibrium
penetrative convection
porous media
stability analysis

ASJC Scopus subject areas

General Engineering
General Physics and Astronomy
General Mathematics

Access to Document

10.1098/rspa.2023.0820

Gianfrani2024AAMAccepted author manuscript, 1.12 MBLicence: CC BY

Cite this

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Stability of penetrative convective currents in local thermal non-equilibrium

Abstract

Bibliographical note

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Funding

Keywords

ASJC Scopus subject areas

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