The instability of a viscoelastic fluid saturating a horizontal porous layer heated from below is studied theoretically with a dynamical system approach. The viscoelastic character of the flow is taken into account by a modified Darcy's law. The conservation equations of mass, momentum and energy are approximated by a reduced-order system of nonlinear, ordinary differential equations, which is similar to the well-known system derived by Lorenz to describe atmospheric convection. Equilibrium points and their stability are expressed as functions of a dimensionless heat capacity and of two relaxation parameters. Qualitative expressions of the Nusselt number when the system is out of equilibrium are also derived.

Thermal instability of viscoelastic fluids in horizontal porous layers as initial value problem / Cafaro, Emilio; Bertola, V.. - In: INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER. - ISSN 0017-9310. - 49:21-22(2006), pp. 4003-4012. [10.1016/j.ijheatmasstransfer.2006.04.006]

Thermal instability of viscoelastic fluids in horizontal porous layers as initial value problem

CAFARO, EMILIO;
2006

Abstract

The instability of a viscoelastic fluid saturating a horizontal porous layer heated from below is studied theoretically with a dynamical system approach. The viscoelastic character of the flow is taken into account by a modified Darcy's law. The conservation equations of mass, momentum and energy are approximated by a reduced-order system of nonlinear, ordinary differential equations, which is similar to the well-known system derived by Lorenz to describe atmospheric convection. Equilibrium points and their stability are expressed as functions of a dimensionless heat capacity and of two relaxation parameters. Qualitative expressions of the Nusselt number when the system is out of equilibrium are also derived.
File in questo prodotto:
Non ci sono file associati a questo prodotto.
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/1529137
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo