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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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
Early online date16 Jun 2021
Publication statusPublished - 31 Oct 2021


  • 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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