Weakly Nonlinear Convection in a Porous Layer with Multiple Horizontal Partitions

Creative Commons License

Rees D. A. S., Bassom A. P., GENÇ G.

TRANSPORT IN POROUS MEDIA, cilt.103, sa.3, ss.437-448, 2014 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 103 Sayı: 3
  • Basım Tarihi: 2014
  • Doi Numarası: 10.1007/s11242-014-0310-y
  • Dergi Adı: TRANSPORT IN POROUS MEDIA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.437-448
  • Anahtar Kelimeler: Porous media, Layered medium, Convection, Weakly nonlinear theory, Pattern selection
  • Erciyes Üniversitesi Adresli: Evet

Özet

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.

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.