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 languageEnglish
Article number121538
JournalInternational Journal of Heat and Mass Transfer
Volume177
Early online date16 Jun 2021
DOIs
Publication statusPublished - 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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