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Research Papers: Porous Media

Effect of Gravity Modulation on Electrothermal Convection in a Dielectric Fluid Saturated Anisotropic Porous Layer

[+] Author and Article Information
Mahantesh S. Swamy

Department of Mathematics,
Government College,
Gulbarga 585 105, India
e-mail: mssmaths@gmail.com

I. S. Shivakumara

Department of Mathematics,
Bangalore University,
Bangalore 560 001, India

N. B. Naduvinamani

Department of Mathematics,
Gulbarga University,
Gulbarga 585 106, India

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received June 2, 2013; final manuscript received October 2, 2013; published online November 28, 2013. Assoc. Editor: Andrey Kuznetsov.

J. Heat Transfer 136(3), 032601 (Nov 28, 2013) (10 pages) Paper No: HT-13-1276; doi: 10.1115/1.4025684 History: Received June 02, 2013; Revised October 02, 2013

This paper deals with linear and nonlinear stability analyses of thermal convection in a dielectric fluid saturated anisotropic Brinkman porous layer subject to the combined effect of AC electric field and time-periodic gravity modulation (GM). In the realm of linear theory, the critical stability parameters are computed by regular perturbation method. The local nonlinear theory based on truncated Fourier series method gives the information of convection amplitudes and heat transfer. Principle of exchange of stabilities is found to be valid and subcritical instability is ruled out. Based on the governing linear autonomous system several qualitative results on stability are discussed. The sensitive dependence of the solution of Lorenz system of electrothermal convection to the choice of initial conditions points to the possibility of chaos. Low frequency g-jitter is found to have significant stabilizing influence which is in turn diminished by an imposed AC electric field. The role of other governing parameters on the stability threshold and on transient heat transfer is determined.

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References

Jones, T. B., 1978, Electrohydrodynamically Enhanced Heat Transfer in Liquids-A Review in Advances in Heat Transfer, T. F.Irvine, Jr. and J. P.Hartnett, eds., Academic Press, New York, pp. 107–144.
Saville, D. A., 1997, “Electrohydrodynamics: The Taylor–Melcher Leaky Dielectric Model,” Annu. Rev. Fluid Mech., 29, pp. 27–64. [CrossRef]
Douiebe, A., Hannaoui, M., Lebon, G., Benaboud, A., and Khmou, A., 2001, “Effects of A.C. Electric Field and Rotation on Benard–Marangoni Convection Flow,” Turbul. Combust., 67, pp. 185–204. [CrossRef]
Othman, M. I. A., and Zaki, S. A., 2003, “The Effect of Thermal Relaxation Time on an Electrohydrodynamic Viscoelastic Fluid Layer Heated From Below,” Can. J. Phys., 81, pp. 779–787. [CrossRef]
Chang, M. H., Ruo, A. C., and Chen, F., 2009, “Electrohydrodynamic instability in A Horizontal Fluid Layer with Electrical Conductivity Gradient Subject to a Weak Shear Flow,” J. Fluid Mech., 634, pp. 191–215. [CrossRef]
Ruo, A. C., Chang, M. H., and Chen, F., 2010, “Effect Of Rotation on the Electrohydrodynamic instability of a Fluid Layer with an Electrical Conductivity Gradient,” Phys. Fluids, 22, p. 024102. [CrossRef]
Del Río, J. A., and Whitaker, S., 2001, “Electrohydrodynamics in Porous Media,” Transp. Porous Media, 44, pp. 385–405. [CrossRef]
El-Sayed, M. F., 2008, “Onset of Electroconvective instability of Oldroydian Viscoelastic Liquid Layer in Brinkman Porous Medium,” Arch. Appl. Mech., 78, pp. 211–224. [CrossRef]
El-Sayed, M. F., Moatimid, G. M., and Metwaly, T. M. N., 2011, “Nonlinear Electrohydrodynamic Stability of Two Superposed Streaming Finite Dielectric Fluids in Porous Medium With interfacial Surface Charges,” Transp. Porous Media, 86, pp. 559–578. [CrossRef]
Shivakumara, I. S., Ng, C., and Nagashree, M. S., 2011, “The Onset of Electrothermoconvection in a Rotating Brinkman Porous Layer,” Int. J. Eng. Sci., 49, pp. 646–663. [CrossRef]
Shivakumara, I. S., Rudraiah, N., Lee, J., and Hemalatha, K., 2011, “The Onset of Darcy-Brinkman Electroconvection in a Dielectric Fluid Saturated Porous Layer,” Transp. Porous Media, 90, pp. 509–528. [CrossRef]
Gresho, P. M., and Sani, R. L., 1970, “The Effect of Gravity Modulation on the Stability of a Heated Fluid Layer,” J. Fluid Mech., 40, pp. 783–806. [CrossRef]
Gershuni, G. Z., Zhukhovitskii, E. M., and Iurkov, I. S., 1970, “On Convective Stability in The Presence Of Periodically Varying Parameter,” J. Appl. Math. Mech., 34, pp. 442–452. [CrossRef]
Malashetty, M. S., and Padmavathi, V., 1997, “Effect of Gravity Modulation on the Onset of Convection in Fluid and Porous Layer,” Int. J. Eng. Sci., 35, pp. 829–840. [CrossRef]
Zen'kovskaya, S. M., and Rogovenko, T. N., 1999, “Filtration Convection in a High-Frequency Vibration Field,” J. Appl. Mech. Tech. Phys., 40, pp. 379–385. [CrossRef]
Bardan, G., and Mojtabi, A., 2000, “On the Horton-Rogers-Lapwood Convective instability with Vertical Vibration,” Phys. Fluids, 12, pp. 2723–2731. [CrossRef]
Rees, D. A. S., and Pop, I., 2000, “The Effect of G-Jitter on Vertical Free Convection Boundary-Layer Flow in Porous Media,” Int. Commun. Heat Mass Transfer27(3), pp. 415–424. [CrossRef]
Rees, D. A. S., and Pop, I., 2001, “The Effect of G-Jitter on Free Convection near a Stagnation Point in a Porous Medium,” Int. J. Heat Mass Transf.44, pp. 877–883. [CrossRef]
Rees, D. A. S., and Pop, I., 2003, “The Effect of Large-Amplitude G-Jitter Vertical Free Convection Boundary-Layer Flow in Porous Media,” Int. J. Heat Mass Transf.46, pp. 1097–1102. [CrossRef]
Govender, S., 2003, “Oscillatory Convection Induced by Gravity and Centrifugal Forces in a Rotating Porous Layer Distant From the Axis of Rotation,” Int. J. Eng. Sci., 41(6), pp. 539–545. [CrossRef]
Govender, S., 2004, “Stability Of Convection in a Gravity Modulated Porous Layer Heated From Below,” Transp. Porous Media, 57(1), pp. 113–123. [CrossRef]
Govender, S., 2005, “Destabilising a Fluid Saturated Gravity Modulated Porous Layer Heated From above,” Transp. Porous Media, 59(2), pp. 215–225. [CrossRef]
Govender, S., 2005, “Weak Non-Linear Analysis of Convection in a Gravity Modulated Porous Layer,” Transp. Porous Media, 60(1), pp. 33–42. [CrossRef]
Govender, S., 2005, “Linear Stability and Convection in a Gravity Modulated Porous Layer Heated From Below: Transition From Synchronous To Subharmonic Solution,” Transp. Porous Media, 59(2), pp. 227–238. [CrossRef]
Govender, S., 2006, “Stability Of Gravity Driven Convection in a Cylindrical Porous Layer Subjected to Vibration,” Transp. Porous Media, 63, pp. 489–502. [CrossRef]
Govender, S., 2010, “Vadasz Number influence On Vibration in a Rotating Porous Layer Placed Far Away From The Axis of Rotation,” ASME J. Heat Transfer, 132, pp. 112601-1-5. [CrossRef]
Kuznetsov, A. V., 2005, “The Onset of Bioconvection in a Suspension of Negatively Geotactic Microorganisms with High–Frequency Vertical Vibration,” Int. Commun. Heat Mass Transfer, 32, pp. 1119–1127. [CrossRef]
Kuznetsov, A. V., 2006, “Linear Stability Analysis of the Effect of Vertical Vibration on Bioconvection in a Horizontal Porous Layer of Finite Depth,” J. Porous Media, 9(6) pp. 597–608. [CrossRef]
Kuznetsov, A. V., 2006, “investigation of the Onset of Bioconvection in a Suspension of Oxytactic Microorganisms Subjected to High-Frequency Vertical Vibration,” Theor. Comput. Fluid Dyn., 20, pp. 73–87. [CrossRef]
Malashetty, M. S., and Swamy, M. S., 2011, “Effect Of Gravity Modulation On The Onset Of Thermal Convection in Rotating Fluid and Porous Layer,” Phys. Fluids, 23, p. 064108. [CrossRef]
Swamy, M. S., Shivakumara, I. S., and Sidram, W., 2013, “The Onset of Convection in a Gravity Modulated Viscoelastic Fluid-Saturated Anisotropic Porous Layer,” Special Topics Rev. Porous Media, 4(1), pp. 69–80. [CrossRef]
Swamy, M. S., 2013, “Effect of Vertical Vibrations on the Onset of Binary Convection,” Int. J. Appl. Mech. Eng., 18(3), pp. 899–910. [CrossRef]
Castinel, G., and Combarnous, M., 1974, “Critere D' Apparitition De La Convection Naturelle Dans Une Couche Poreuse Anisotrope Horizontale,” C. R. Acad. Sci. B., 278, pp. 701–704.
Epherre, J. F., 1975, “Critere D'' Apparitition De La Convection Naturelle Dans Une Couche Poreuse Anisotrope,” Rev. Gen. Therm., 168, pp. 949–950.
Kvernvold, O., and Tyvand, P. A., 1979, “Nonlinear Thermal Convection in Anisotropic Porous Media,” J. Fluid Mech., 90, pp. 609–662. [CrossRef]
Nilsen, T., and Storesletten, L., 1990, “An Analytical Study on Natural Convection in Isotropic and Anisotropic Channels,” ASME J. Heat Transfer, 112, pp. 396–401. [CrossRef]
Nield, D. A., and Bejan, A., 2006, Convection in Porous Media, 3rd ed., Springer, New York.
Venezian, G., 1969, “Effect of Modulation on the Onset of Thermal Convection,” J. Fluid Mech., 35, pp. 243–254. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Variation of correction Rayleigh number with frequency for different values of RaE and Da

Grahic Jump Location
Fig. 2

Variation of correction Rayleigh number with frequency for different values of ξ and RaE

Grahic Jump Location
Fig. 3

Variation of correction Rayleigh number with frequency for different values of η and RaE

Grahic Jump Location
Fig. 4

Variation of correction Rayleigh number with frequency for different values of χ and M

Grahic Jump Location
Fig. 5

Variation of Nusselt number with time for different (a) amplitude, (b) frequency, (c) RaE and (d) Da

Grahic Jump Location
Fig. 6

Variation of Nusselt number with time for different (a) ξ, (b) η, (c) M, and (d) χ

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