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International Heat Transfer Conference 13
Graham de Vahl Davis (open in a new tab) School of Mechanical and Manufacturing Engineering, University of New South Wales, Kensington, NSW, Australia
Eddie Leonardi (open in a new tab) Computational Fluid Dynamics Research Laboratory, School of Mechanical and Manufacturing Engineering, The University of New South Wales, Sydney, Australia 2052

ISSN Online: 2377-424X

ISBN CD: 1-56700-226-9

ISBN Online: 1-56700-225-0

THE INFLUENCE OF MECHANICAL VIBRATIONS ON CONVECTIVE MOTION IN A CONFINED POROUS CAVITY: HARMONIC AND SUB-HARMONIC RESPONSES

page 12
DOI: 10.1615/IHTC13.p5.230
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ABSTRACT

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.

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