Article
Rotating Brinkman–Lapwood Convection with Modulation
Transport in Porous Media (Impact Factor: 1.55). 01/2011; 88(3):369383. DOI: 10.1007/s1124201197447
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Article: Stabilite d'une couche poreuse horizontale soumise a des conditions aux limites periodiques
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ABSTRACT: The stability of a horizontal porous layer, the temperature of which at the inner side is a periodical function of time, has been theoretically studied by the Galerkin technique. The results show a correlation between the Rayleigh number, the reduced frequency of the signal on the wall and its amplitude. Different types of evolution of the instabilities within the porous layer are observed and two critical Rayleigh numbers can be defined, which correspond to the boundary states separating the unconditionally steady states, the globally steady states and the unsteady states.ZusammenfassungDie Stabilität einer porösen Horizontalschicht, deren Temperatur auf der Bodenfläche eine periodische Zeitfunktion ist, wurde mittels der GalerkinMethode theoretisch untersucht. Die Ergebnisse zeigen eine Korrelation zwischen der RayleighZahl, der reduzierten Frequenz des Signals auf der Fläche und seiner Amplitude. Es werden verschiedene Entwicklungstypen der Unstabilitäten innerhalb der porösen Schicht beobachtet und zwei kritische RayleighZahlen bestimmt, entsprechend den Grenzzuständen, die die unbedingt stabilen Zustände, die im Ganzen stabilen Zustände und die unstabilen Zustände abgrenzen.РефератYcтoйчивocть гopизoнтaльнoгo пopиcтoгo cлoя, тeмпepaтypa нижнeгo cлoя кoтopoгo являeтcя пepиoдичecкoй фyнкциeй вpeмeни, былa тeopeтичecки изyчeнa мeтoдoм Гaлepкинa. Peзyльтaты пoкaзывaют зaвиcимocть мeждy чиcлoм Pэлeя, пpивeдiннoй чacтoтoй cигнaлa нa cтeнкe и aмплитyдoй cигнaлa. Былo oтмeчeнo нecкoлькo типoв эвoлюции нeycтoйчивocтeй внyтpи пopиcтoгo cлcтя и ycтaнoвлeнo двa кpитичecкич чиcлa pэлeя, cooтвeтcтвyющич гpaничным cocтoяниям, paздeляющим aбcoлютнo ycтoйчивoe, глoбaльнo ycтoйчивoe и нeycтoйчивoe cocтoяния.International Journal of Heat and Mass Transfer  INT J HEAT MASS TRANSFER. 01/1976; 19(8):815820.  [Show abstract] [Hide abstract]
ABSTRACT: Linear stability and weak nonlinear theories are used to investigate analytically the Coriolis effect on threedimensional gravitydriven convection in a rotating porous layer heated from below. Major differences as well as similarities with the corresponding problem in pure fluids (nonporous domains) are particularly highlighted. As such, it is found that, in contrast to the problem in pure fluids, overstable convection in porous media is not limited to a particular domain of Prandtl number values (in pure fluids the necessary condition is Pr<1). Moreover, it is also established that in the porousmedia problem the critical wavenumber in the plane containing the streamlines for stationary convection is not identical to the critical wavenumber associated with convection without rotation, and is therefore not independent of rotation, a result which is quite distinct from the corresponding purefluids problem. Nevertheless it is evident that in porous media, just as in the case of pure fluids subject to rotation and heated from below, the viscosity at high rotation rates has a destabilizing effect on the onset of stationary convection, i.e. the higher the viscosity the less stable the fluid. Finiteamplitude results obtained by using a weak nonlinear analysis provide differential equations for the amplitude, corresponding to both stationary and overstable convection. These amplitude equations permit one to identify from the posttransient conditions that the fluid is subject to a pitchfork bifurcation in the stationary convection case and to a Hopf bifurcation associated with the overstable convection. Heat transfer results were evaluated from the amplitude solution and are presented in terms of Nusselt number for both stationary and overstable convection. They show that rotation has in general a retarding effect on convective heat transfer, except for a narrow region of small values of the parameter containing the Prandtl number where rotation enhances the heat transfer associated with overstable convection.Journal of Fluid Mechanics 12/1998; 376:351  375. · 2.18 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: In this work, we study the problem of onset of thermal convection in a rotating saturated porous medium heated from below. The effect of rotation is restricted to the Coriolis force, neglecting thus the centrifugal effects, the porous medium is described by Brinkman's model. The linear eigenvalue problem is solved by means of a modified Galerkin method. The behavior of the critical temperature gradient is discussed in terms of various parameters of the system for both stationary and overstable convections. Finally a weakly nonlinear analysis is provided to derive amplitude equations and to study the onset of KüppersLortz instability.Physics of Condensed Matter 01/2002; 29(4):641647. · 1.28 Impact Factor
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