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Natural convection heat transfer in the annular region between porous confocal ellipses
Author(s) -
Saatdjian E.,
Lam R.,
Mota J.P.B.
Publication year - 1999
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/(sici)1097-0363(19990930)31:2<513::aid-fld889>3.0.co;2-7
Subject(s) - mechanics , geometry , annulus (botany) , heat transfer , physics , radius , natural convection , mathematics , classical mechanics , materials science , computer security , computer science , composite material
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. Copyright © 1999 John Wiley & Sons, Ltd.