Weakly Nonlinear Convection in a Porous Layer with Multiple Horizontal Partitions

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Rees D. A. S., Bassom A. P., GENÇ G.

TRANSPORT IN POROUS MEDIA, vol.103, no.3, pp.437-448, 2014 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 103 Issue: 3
  • Publication Date: 2014
  • Doi Number: 10.1007/s11242-014-0310-y
  • Journal Name: TRANSPORT IN POROUS MEDIA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.437-448
  • Keywords: Porous media, Layered medium, Convection, Weakly nonlinear theory, Pattern selection
  • Erciyes University Affiliated: Yes

Abstract

We consider convection in a horizontally uniform fluid-saturated porous layer

which is heated from below and which is split into a number of identical sublayers by

impermeable and infinitesimally thin horizontal partitions. Rees and Genç (Int J Heat Mass

Transfer 54:3081–3089,

 

 

2010) determined the onset criterion by means of a detailed analytical

and numerical study of the corresponding dispersion relation and showed that this layered

system behaves like the single-sublayer constant-heat-flux Darcy–Bénard problem when the

number of sublayers becomes large. The aim of the present work is to use a weakly nonlinear

analysis to determine whether the layered system also shares the property of the singlesublayer

constant-heat-flux Darcy–Bénard problem by having square cells, as opposed to

rolls, as the preferred planform for convection.

We consider convection in a horizontally uniform fluid-saturated porous layer which is heated from below and which is split into a number of identical sublayers by impermeable and infinitesimally thin horizontal partitions. Rees and Genc (Int J Heat Mass Transfer 54:3081-3089, 2010) determined the onset criterion by means of a detailed analytical and numerical study of the corresponding dispersion relation and showed that this layered system behaves like the single-sublayer constant-heat-flux Darcy-Benard problem when the number of sublayers becomes large. The aim of the present work is to use a weakly nonlinear analysis to determine whether the layered system also shares the property of the single-sublayer constant-heat-flux Darcy-Benard problem by having square cells, as opposed to rolls, as the preferred planform for convection.