Publication de 12 numéros par an
ISSN Imprimer: 1091-028X
ISSN En ligne: 1934-0508
Indexed in
STATIONARY CONVECTION IN A CYLINDRICAL POROUS LAYER SUBJECTED TO G-GITTER
RÉSUMÉ
An analytical investigation for the onset of convection in a vertical fluid-saturated cylindrical porous layer is presented when gravity-modulated vibration (g-gitter) is present. For the current configuration, the temperature gradient is colinear with the plane of the vibration. A linear stability analysis is used to determine the convection threshold in terms of the critical Rayleigh number, and a comparison is made with the critical Rayleigh number computed for the rectangular porous layer subjected to vibration. The results indicate that the presence of vibration stabilizes the convection (i.e., increases the magnitude of the Rayleigh number) across the range vibration frequencies. Of particular interest is the fact that for stationary convection, the frequency bandwidth for convection is smaller for the rectangular porous layer than for the cylindrical porous layer, thus indicating the effect of geometry on stability criteria.
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Bardan, G. and Mojtabi, A., On the Horton-Rogers-Lapwood Convective Instability with Vertical Vibration: Onset of Convection, Phys. Fluids, vol. 12, pp. 2723-2731, 2000.
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Bardan, G., Razi, Y.P., and Mojtabi, A., Comments on the Mean Flow Averaged Model, Phys. Fluids, vol. 16, pp. 4535-4538, 2004.
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Chandrasekhar, S., Ed., Hydrodynamic andHydromagnetic Stability, Oxford, UK: Oxford University Press, 1961.
-
Christov, C.I. and Homsy, G.M., Nonlinear Dynamics of Two-Dimensional Convection in a Vertically Stratified Slot with and without Gravity Modulation, J. FluidMech., vol. 430, pp. 335-360, 2001.
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Faraday, M., On Peculiar Class of Acoustical Figures, and on Certain Forms Assumed by Groups of Particles upon Vibrating Elastic Surfaces, Philos. Trans. R. Soc. London, vol. 121, pp. 299-340, 1831.
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Gershuni, G.Z., Zhukhovitskiy, E.M., and Iurkov, S., On Convective Stability in the Presence of Periodically Varying Parameter, J. Appl. Math. Mech, vol. 34, pp. 470-480, 1970.
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Gershuni, G.Z. and Luyibimov, D.U., Thermal Vibrational Convection, New York: Wiley, 1998.
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Govender, S., Stability of Convection in a Gravity Modulated Porous Layer Heated from below, Transp. Porous Media, vol. 57, no. 1,pp. 113-123,2004.
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Govender, S., Linear Stability and Convection in a Gravity Modulated Porous Layer Heated from below: Transition from Synchronous to Sub-Harmonic Solutions, Transp. Porous Media, vol. 59, no. 2, pp. 227-238, 2005a.
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Govender, S., Stability Analysis of a Porous Layer Heated from below and Subjected to Low Frequency Vibration: Frozen Time Analysis, Transp. Porous Media, vol. 59, no. 2, pp. 239-247, 2005b.
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Govender, S., Weak Non-Linear Analysis of Convection in a Gravity Modulated Porous Layer, Transp. Porous Media, vol. 60, no. 1,pp. 33-42, 2005c.
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Govender, S., Stability of Gravity Driven Convection in a Cylindrical Porous Layer Subjected to Vibration, Transp. Porous Media, vol. 63, pp. 489-502, 2006.
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Gresho, P.M. and Sani, R.L., The Effects of Gravity Modulation on the Stability of a Heated Fluid Layer, J. Fluid Mech, vol. 40, pp. 783-806, 1970.
-
Hirata, K., Sasaki, T., and Tanigawa, H., Vibrational Effect on Convection in a Square Cavity at Zero Gravity, J. Fluid Mech., vol. 445, pp. 327-344,2001.
-
Nield, D.A. and Bejan, A., Convection in a Porous Medium, New York: Springer, 2013.
-
Wadih, M. and Roux, B., Natural Convection in a Long Vertical Cylinder under Gravity Modulation, J. Fluid Mech, vol. 193, pp. 391-415, 1988.
-
Zebib, A., Onset of Natural Convection in a Cylinder of Water Saturated Porous Media, Phys. Fluids, vol. 21, pp. 699-700,1978.