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International Heat Transfer Conference 13

ISBN Imprimer: 1-56700-226-9 (CD)
ISBN En ligne: 1-56700-225-0


DOI: 10.1615/IHTC13.p5.230
page 12

Marie-Catherine Charrier-Mojtabi
Laboratoire PHASE E.A. 3028, Université Paul Sabatier, France

Y. P. Razi
IMFT, UMR CNRS/INP/UPS N°5502, Université Paul Sabatier, France

Abdelkader Mojtabi
Institut de Mecanique des Fluides, UMR CNRS-INP-UPS №5502 Universite Paul Sabatier, 118 route de Narbonne, F 31062 Toulouse, Cedex France.


This paper deals with the onset of convection in a rectangular enclosure filled with a porous medium saturated by a pure fluid under the action of mechanical vibrations. The enclosure is heated from below and its lateral boundaries are thermally insulated. Vibrations are considered to be harmonic and their direction are parallel to the temperature gradient. The time-dependent Darcy model is used in the momentum equation. The problem depends on four dimensionless parameters: the filtration thermal Rayleigh number, RaT, the vibrational Rayleigh number, Rav, the transient coefficient in the Darcy equation, B, and the aspect ratio of the cell, AL (AL = H/L with H the height of the cavity and L its length). Linear stability analysis is performed, which leads us to a Mathieu equation. This equation is solved using Floquet theory. Several cases based on frequency of vibration are considered: high frequency with small amplitude (harmonic response) or high frequency with arbitrary amplitude (sub- harmonic response). The critical values for the onset of convection corresponding to harmonic and sub-harmonic solutions are represented in a RaTc-ω diagram. For high frequency and small amplitude vibrations, analytical relations are found, from which we obtain the critical values of the thermal Rayleigh number and the corresponding convective patterns. For the harmonic solutions our results show that vibrations decrease the number of convective rolls and increase the critical Rayleigh number. An analogy is found with the Mathieu equation governing thermal stability results of an infinite layer, which simplifies the computations. For the case of time-averaged formulation, numerical calculations are performed with a spectral code and corroborate the analytical results.

IHTC-13 Digital Library

Measurement of fluid temperature with an arrangement of three thermocouples FLOW BOILING OF A HIGHLY VISCOUS POLYMER SOLUTION