On the stability of the isoflux Darcy–Bénard problem with a generalised basic state

P. V. Brandão; A. Barletta; M. Celli; L. S. de B Alves; D. A.S. Rees

doi:10.1016/j.ijheatmasstransfer.2021.121538

On the stability of the isoflux Darcy–Bénard problem with a generalised basic state

P. V. Brandão, A. Barletta, M. Celli, L. S. de B Alves, D. A.S. Rees

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Abstract

The scope of this study is to determine the conditions for the onset of the instability in a horizontal porous layer subject to isoflux boundary conditions and with an infinitely wide single–cell basic flow. When the circulation in the basic cellular flow is absent, one recovers the usual Darcy–Bénard conduction basic state. The governing parameters are the Rayleigh number associated with the uniform wall heat flux, and the dimensionless horizontal temperature gradient. The latter parameter controls the magnitude of the basic cellular circulation flow in the horizontal direction. The modal analysis of the instability is carried out numerically by employing a pseudo–spectral method, as well as the shooting method for the solution of the stability eigenvalue problem. Neutral stability and the critical conditions for the onset of the convective instability of the basic state are investigated.

Original language	English
Article number	121538
Journal	International Journal of Heat and Mass Transfer
Volume	177
Early online date	16 Jun 2021
DOIs	https://doi.org/10.1016/j.ijheatmasstransfer.2021.121538
Publication status	Published - 31 Oct 2021

Bibliographical note

Funding Information:
The authors A. Barletta and M. Celli acknowledge the financial support from the grant PRIN 2017F7KZWS provided by the Italian Ministry of Education and Scientific Research. The author P. V. Brand?o acknowledges the financial support from Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior - Brasil (CAPES) - Grant 88881. 174085/2018-01.

Funding Information:
The authors A. Barletta and M. Celli acknowledge the financial support from the grant PRIN 2017F7KZWS provided by the Italian Ministry of Education and Scientific Research. The author P. V. Brandão acknowledges the financial support from Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Grant 88881. 174085/2018-01.

Funding

The authors A. Barletta and M. Celli acknowledge the financial support from the grant PRIN 2017F7KZWS provided by the Italian Ministry of Education and Scientific Research. The author P. V. Brand?o acknowledges the financial support from Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior - Brasil (CAPES) - Grant 88881. 174085/2018-01. The authors A. Barletta and M. Celli acknowledge the financial support from the grant PRIN 2017F7KZWS provided by the Italian Ministry of Education and Scientific Research. The author P. V. Brandão acknowledges the financial support from Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Grant 88881. 174085/2018-01.

Keywords

Hadley flow
Natural convection
Porous medium
Pseudo-spectral method
Rayleigh number
Stability analysis

ASJC Scopus subject areas

Condensed Matter Physics
Mechanical Engineering
Fluid Flow and Transfer Processes

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10.1016/j.ijheatmasstransfer.2021.121538

paper184.acceptedAccepted author manuscript, 3.56 MBLicence: CC BY-NC-ND

Cite this

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title = "On the stability of the isoflux Darcy–B{\'e}nard problem with a generalised basic state",

abstract = "The scope of this study is to determine the conditions for the onset of the instability in a horizontal porous layer subject to isoflux boundary conditions and with an infinitely wide single–cell basic flow. When the circulation in the basic cellular flow is absent, one recovers the usual Darcy–B{\'e}nard conduction basic state. The governing parameters are the Rayleigh number associated with the uniform wall heat flux, and the dimensionless horizontal temperature gradient. The latter parameter controls the magnitude of the basic cellular circulation flow in the horizontal direction. The modal analysis of the instability is carried out numerically by employing a pseudo–spectral method, as well as the shooting method for the solution of the stability eigenvalue problem. Neutral stability and the critical conditions for the onset of the convective instability of the basic state are investigated.",

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note = "Funding Information: The authors A. Barletta and M. Celli acknowledge the financial support from the grant PRIN 2017F7KZWS provided by the Italian Ministry of Education and Scientific Research. The author P. V. Brand?o acknowledges the financial support from Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior - Brasil (CAPES) - Grant 88881. 174085/2018-01. Funding Information: The authors A. Barletta and M. Celli acknowledge the financial support from the grant PRIN 2017F7KZWS provided by the Italian Ministry of Education and Scientific Research. The author P. V. Brand{\~a}o acknowledges the financial support from Coordena{\c c}{\~a}o de Aperfei{\c c}oamento de Pessoal de N{\'i}vel Superior - Brasil (CAPES) - Grant 88881. 174085/2018-01. ",

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AU - Rees, D. A.S.

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PY - 2021/10/31

Y1 - 2021/10/31

N2 - The scope of this study is to determine the conditions for the onset of the instability in a horizontal porous layer subject to isoflux boundary conditions and with an infinitely wide single–cell basic flow. When the circulation in the basic cellular flow is absent, one recovers the usual Darcy–Bénard conduction basic state. The governing parameters are the Rayleigh number associated with the uniform wall heat flux, and the dimensionless horizontal temperature gradient. The latter parameter controls the magnitude of the basic cellular circulation flow in the horizontal direction. The modal analysis of the instability is carried out numerically by employing a pseudo–spectral method, as well as the shooting method for the solution of the stability eigenvalue problem. Neutral stability and the critical conditions for the onset of the convective instability of the basic state are investigated.

AB - The scope of this study is to determine the conditions for the onset of the instability in a horizontal porous layer subject to isoflux boundary conditions and with an infinitely wide single–cell basic flow. When the circulation in the basic cellular flow is absent, one recovers the usual Darcy–Bénard conduction basic state. The governing parameters are the Rayleigh number associated with the uniform wall heat flux, and the dimensionless horizontal temperature gradient. The latter parameter controls the magnitude of the basic cellular circulation flow in the horizontal direction. The modal analysis of the instability is carried out numerically by employing a pseudo–spectral method, as well as the shooting method for the solution of the stability eigenvalue problem. Neutral stability and the critical conditions for the onset of the convective instability of the basic state are investigated.

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On the stability of the isoflux Darcy–Bénard problem with a generalised basic state

Abstract

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

Access to Document

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