Natural convection heat transfer in the annular region between porous confocal ellipses

E. Saatdjian, R. Lam, João P. B. Mota

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


The Darcy-Boussinesq equations are solved in two dimensions and in elliptical cylindrical co-ordinates using a second-order-accurate finite difference code and a very fine grid. For the limiting case of a circular geometry, the results show that a hysteresis loop is possible for some values of the radius ratio, in agreement both with previous calculations using cylindrical co-ordinates and with the available experimental data. For the general case of an annulus of elliptical cross-section, two configurations, blunt or slender, are considered. When the major axes are horizontal (blunt case) a hysteresis loop appears for a certain range of Raleigh numbers. For the slender configuration, when the major axes are vertical, a transition from a steady to a periodic regime (Hopf bifurcation) has been evidenced. In all cases, the heat transfer rate from the slender geometry is greater than that obtained in the blunt case.

Original languageEnglish
Pages (from-to)513-522
Number of pages10
JournalInternational Journal For Numerical Methods In Fluids
Issue number2
Publication statusPublished - 1 Sept 1999


  • Darcy-Boussinesq equations
  • Natural convection
  • Porous confocal ellipses


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