An electroconvection in a horizontal dielectric fluid saturated with a densely packed porous layer is investigated under the simultaneous action of vertical electric field and vertical temperature gradient when the walls of the layer are subjected to time periodic temperature modulation. The dielectric constant is assumed to be a linear function of temperature. A regular perturbation method based on small amplitude of applied temperature field is used to compute the critical values of Rayleigh number and wave number. The shift in the critical Rayleigh number is calculated as a function of frequency of modulation, electric Rayleigh number, Prandtl number, and Darcy number, and their effects on the critical Rayleigh number are discussed. The situations which are favorable for the design of artificial organs without the side effect of hemolysis are explained.
Issue Section:
Research Papers
1.
Christopherson
, D. C.
, and Dowson
, D.
, 1959, “An Example of Minimum Energy Dissipation of Viscous Flow
,” Proc. R. Soc. London, Ser. A
0950-1207, 251
, pp. 550
–564
.2.
Sri Rammurthy
, A. M.
, and Arunachalam
, V. S.
, 1982, Eutectic Growth in Space
, S.
Ramaseshan
and M. K.
Tiwari
, eds., Indian Academy of Sciences
, India
, pp. 195
–207
.3.
Joseph
, D. D.
, 1976, “Stability of Fluid Motions I & II
,” Springer Tracts in Natural Philosophy
, Vol. 28
, Springer
, New York
.4.
Cheng
, P.
, 1978, “Heat Transfer in Geothermal Systems
,” Advances in Heat Transfer
, Vol. 14
, Academic Press
, New York
, pp. 1
–105
.5.
Caltagirone
, J. P.
, 1981, “Convection in a Porous Medium
,” Convective Transport and Instability Phenomena
, G.
Braun
, ed., Karlsruhe
, Germany
, pp. 199
–232
.6.
Rudraiah
, N.
, and Balachandra Rao
, S.
, 1982, “Nonlinear Cellular Convection and Heat Transport in a Porous Medium
,” Appl. Sci. Res.
0003-6994, 39
, pp. 21
–43
.7.
Rudraiah
, N.
, and Balachandra Rao
, S.
, 1983, “Study of Nonlinear Convection in a Sparsely Packed Porous Medium Using Spectral Analysis
,” Appl. Sci. Res.
0003-6994, 40
(3
), pp. 223
–245
.8.
Roberts
, P. H.
, 1969, “Electrohydrodynamic Convection
,” Q. J. Mech. Appl. Math.
0033-5614, 22
, pp. 211
–220
.9.
Takashima
, M.
, and Aldridge
, K. D.
, 1976, “The Stability of a Horizontal Layer of Dielectric Fluid Under the Simultaneous Action of a Vertical DC Electric Field and Vertical Temperature Gradient
,” Q. J. Mech. Appl. Math.
0033-5614, 29
, pp. 71
–87
.10.
Bradley
, R.
, 1978, “Overstable Electroconvective Instabilities
,” Q. J. Mech. Appl. Math.
0033-5614, 31
, pp. 381
–390
.11.
Wong
, J.
, and Melcher
, J. R.
, 1969, “Thermally Induced Electroconvection
,” Phys. Fluids
0031-9171, 12
, pp. 2264
–2269
.12.
Venezian
, G.
, 1969, “Effect of Modulation on the Onset of Thermal Convection
,” J. Fluid Mech.
0022-1120, 35
, pp. 243
–254
.13.
Rosenblat
, S.
, and Herbert
, D. M.
, 1970, “Low Frequency Modulation of Thermal Instability
,” J. Fluid Mech.
0022-1120, 43
, pp. 385
–398
.14.
Finucane
, R. G.
, and Kelly
, R. E.
, 1976, “Onset of Instability in a Fluid Layer Heated Sinusoidaly From Below
,” Int. J. Heat Mass Transfer
0017-9310, 19
, pp. 71
–85
.15.
Nield
, D. A.
, 1975, “The Onset of Transient Convective Instability
,” J. Fluid Mech.
0022-1120, 71
, pp. 441
–454
.16.
Rudraiah
, N.
, Kaloni
, P. N.
, and Radhadevi
, P. V.
, 1990, “Effect of Modulation on the Onset of Thermal Convection in a Viscoelastic Fluid-Saturated Sparsely Packed Porous Layer
,” Can. J. Phys.
0008-4204, 68
(2
), pp. 214
–221
.17.
Rudraiah
, N.
, Veerappa
, B.
, and Balachandra Rao
, S.
, 1980, “Effect of Non-Uniform Thermal Gradinet and Adiabatic Boundaries on Convection in a Porous Media
,” ASME J. Heat Transfer
0022-1481, 102
(2
), pp. 254
–260
.18.
Rudraiah
, N.
, Ramachandramurthy
, V.
, and Chandana
, O. P.
, 1985, “Effects of Magnetic Field and Nonuniform Temperature Gradient on Marangoni Convection
,” Int. J. Heat Mass Transfer
0017-9310, 28
(8
), pp. 1621
–1624
.19.
Rudraiah
, N.
, and Chandana
, O. P.
, 1985, “Effects of Coriolis Force and Nonuniform Temperature Gradient on Rayleigh Benard Convection
,” Can. J. Phys.
0008-4204, 64
, pp. 90
–99
.20.
Gross
, M. J.
, and Porter
, J. E.
, 1966, “Electrically Induced Convection in Dielectric Liquids
,” Nature (London)
0028-0836, 212
, pp. 1343
–1345
.21.
Gross
, M. J.
, 1967, Mantles of the Earth and Terrestrial Planets
, S. K.
Runcom
, ed., Wiley
, New York
.22.
Rosenblat
, S.
, and Tanaka
, G. A.
, 1971, “Modulation of Thermal Convective Instability
,” Phys. Fluids
0031-9171, 14
, pp. 1319
–1322
.23.
Roppo
, M. H.
, Davis
, S. H.
, and Rosenblat
, S.
, 1984, “Benard Convection With Time Periodic Heating
,” Phys. Fluids
0031-9171, 27
, pp. 796
–803
.24.
Schmitt
, S.
, and Lucke
, M.
, 1991, “Amplitude Equation for Modulated Rayleigh Benard Convection
,” Phys. Rev. A
1050-2947, 44
(8
), pp. 4986
–5002
.25.
Or
, A. C.
, and Kelly
, R. E.
, 1999, “Time Modulated Convection With Zero Mean Temperature Gradient
,” Phys. Rev. E
1063-651X, 60
(2
), pp. 1741
–1747
.26.
Or
, A. C.
, 2001, “Onset Condition of Modulated Rayleigh-Benard at Low Frequency
,” Phys. Rev. E
1063-651X, 64
, p. 050201
.27.
Li
, B. Q.
, 2001, “Stability of Modulated-Gravity-Induced Thermal Convection in Magnetic Fields
,” Phys. Rev. E
1063-651X, 63
, p. 041508
.28.
Lapwood
, E. R.
, 1948, “Convection of a Fluid in a Porous Medium
,” Proc. Cambridge Philos. Soc.
0068-6735, 44
, pp. 508
–521
.Copyright © 2009
by American Society of Mechanical Engineers
You do not currently have access to this content.
