The effect of temperature modulation on the onset of thermal convection in an electrically conducting fluid-saturated-porous medium, heated from below, has been studied using linear stability analysis. The amplitudes of temperature modulation at the lower and upper surfaces are considered to be very small. The porous medium is confined between two horizontal walls and subjected to a vertical magnetic field; flow in porous medium is characterized by Brinkman–Darcy model. Considering only infinitesimal disturbances, and using perturbation procedure, the combined effect of temperature modulation and vertical magnetic field on thermal instability has been studied. The correction in the critical Rayleigh number is calculated as a function of frequency of modulation, Darcy number, Darcy Chandrasekhar number, magnetic Prandtl number, and the nondimensional group number . The influence of the magnetic field is found to be stabilizing. Furthermore, it is also found that the onset of convection can be advanced or delayed by proper tuning of the frequency of modulation. The results of the present model have been compared with that of Darcy model.
Issue Section:
Porous Media
1.
Wallace
, W. E.
, Pierce
, C. I.
, and Sawyer
, W. K.
, 1969, “Experiments on the Flow of Mercury in Porous Media in a Transverse Magnetic Field
,” Bureau of Mines, Report No. RI-7259(PB-184327).2.
Nield
, D. A.
, and Bejan
, A.
, 2006, Convection in Porous Media
, Springer-Verlag
, New York
.3.
Patil
, R. P.
, and Rudraiah
, N.
, 1973, “Stability of Hydromagnetic Thermoconvective Flow Through Porous Medium
,” ASME J. Appl. Mech.
0021-8936, E40
, pp. 879
–884
.4.
Rudraiah
, N.
, and Vortmeyer
, D.
, 1978, “Stability of Finite-Amplitude and Overstable Convection of a Conducting Fluid Through Fixed Porous Bed
,” Waerme- Stoffuebertrag.
0042-9929, 11
, pp. 241
–254
.5.
Rudraiah
, N.
, 1984, “Linear and Non-Linear Megnetoconvection in a Porous Medium
,” Proc. Indian Acad. Sci., Math. Sci.
0253-4142, 93
, pp. 117
–135
.6.
Alchaar
, S.
, Vasseur
, P.
, and Bilgen
, E.
, 1995, “Effect of a Magnetic Field on the Onset of Convection in a Porous Medium
,” Heat Mass Transfer
0947-7411, 30
, pp. 259
–267
.7.
Alchaar
, S.
, Vasseur
, P.
, and Bilgen
, E.
, 1995, “Hydromagnetic Natural Convection in a Tilted Rectangular Porous Enclosure
,” Numer. Heat Transfer, Part A
1040-7782, 27
, pp. 107
–127
.8.
Bian
, W.
, Vasseur
, P.
, and Bilgen
, E.
, 1996, “Effect of an External Magnetic Field on Buoyancy Driven Flow in a Shallow Porous Cavity
,” Numer. Heat Transfer, Part A
1040-7782, 29
, pp. 625
–638
.9.
Bian
, W.
, Vasseur
, P.
, Bilgen
, E.
, and Meng
, F.
, 1996, “Effect of an Electromagnetic Field on Natural Convection in an Inclined Porous Layer
,” Int. J. Heat Fluid Flow
0142-727X, 17
, pp. 36
–44
.10.
Oldenburg
, C. M.
, Borglin
, S. E.
, and Moridis
, G. J.
, 2000, “Numerical Simulation of Ferrofluid Flow for Subsurface Environmental Engineering Applications
,” Transp. Porous Media
0169-3913, 38
, pp. 319
–344
.11.
Borglin
, S. E.
, Moridis
, G. J.
, and Oldenburg
, C. M.
, 2000, “Experimental Studies of Flow of Ferrofluid in Porous Media
,” Transp. Porous Media
0169-3913, 41
, pp. 61
–80
.12.
Sekar
, R.
, Vaidyanathan
, G.
, and Ramanathan
, A.
, 1993, “The Ferroconvection in Fluids Saturating a Rotating Densely Packed Porous Medium
,” Int. J. Eng. Sci.
0020-7225, 31
(2
), pp. 241
–250
.13.
Sekar
, R.
, and Vaidyanathan
, G.
, 1993, “Convective Instability of a Magnetized Ferrofluid in a Rotating Porous Medium
,” Int. J. Eng. Sci.
0020-7225, 31
(8
), pp. 1139
–1150
.14.
Desaive
, T.
, Hennenberg
, M.
, and Dauby
, P. C.
, 2004, “Stabilite Thermomagneto-Convective d’un Ferrofluide dans une Couche Poreuse en Rotation
,” Mecanique & Industries
, 5
, pp. 621
–625
.15.
Sunil
, Divya
, and Sharma
, R. C.
, 2005, “The Effect of Magnetic Field Dependent Viscosity on Thermosolutal Convection in a Ferromagnetic Fluid Saturating a Porous Medium
,” Transp. Porous Media
0169-3913, 60
, pp. 251
–274
.16.
Sunil
, Divya
, and Sharma
, R. C.
, 2004, “Effect of Rotation on Ferromagnetic Fluid Heated and Soluted From Below Saturating a Porous Media
,” J. Geophys. Eng.
1742-2132, 1
, pp. 116
–127
.17.
Saravanan
, S.
, and Yamaguchi
, H.
, 2005, “Onset of Centrifugal Convection in a Magnetic-Fluid-Saturated Porous Medium
,” Phys. Fluids
1070-6631, 17
, p. 084105
.18.
Venezian
, G.
, 1969, “Effect of Modulation on the Onset of Thermal Convection
,” J. Fluid Mech.
0022-1120, 35
(2
), pp. 243
–254
.19.
Rosenblat
, S.
, and Tanaka
, G. A.
, 1971, “Modulation of Thermal Convection Instability
,” Phys. Fluids
0031-9171, 14
(7
), pp. 1319
–1322
.20.
Roppo
, M. N.
, Davis
, S. H.
, and Rosenblat
, S.
, 1984, “Benard Convection With Time-Periodic Heating
,” Phys. Fluids
0031-9171, 27
(4
), pp. 796
–803
.21.
Bhadauria
, B. S.
, and Bhatia
, P. K.
, 2002, “Time-Periodic Heating of Rayleigh-Benard Convection
,” Phys. Scr.
0031-8949, 66
(1
), pp. 59
–65
.22.
Bhadauria
, B. S.
, 2006, “Time-Periodic Heating of Rayleigh-Benard Convection in a Vertical Magnetic Field
,” Phys. Scr.
0031-8949, 73
(3
), pp. 296
–302
.23.
Chhuon
, B.
, and Caltagirone
, J. P.
, 1979, “Stability of a Horizontal Porous Layer With Timewise Periodic Boundary Conditions
,” ASME J. Heat Transfer
0022-1481, 101
, pp. 244
–248
.24.
Rudraiah
, N.
, and Malashetty
, M. S.
, 1990, “Effect of Modulation on the Onset of Convection in a Sparsely Packed Porous Layer
,” ASME J. Heat Transfer
0022-1481, 112
, pp. 685
–689
.25.
Malashetty
, M. S.
, and Basavaraja
, D.
, 2002, “Rayleigh-Benard Convection Subject to Time Dependent Wall Temperature∕Gravity in a Fluid Saturated Anisotropic Porous Medium
,” Heat Mass Transfer
0947-7411, 38
, pp. 551
–563
.26.
Bhadauria
, B. S.
, 2007, “Thermal Modulation of Raleigh-Benard Convection in a Sparsely Packed Porous Medium
,” J. Porous Media
1091-028X, 10
(2
), pp. 175
–188
.27.
Bhadauria
, B. S.
, 2007, “Fluid Convection in a Rotating Porous Layer Under Modulated Temperature on the Boundaries
,” Transp. Porous Media
0169-3913, 67
(2
), pp. 297
–315
.28.
Bhadauria
, B. S.
, 2007, “Magnetofluidconvection in a Rotating Porous Layer Under Modulated Temperature on the Boundaries
,” ASME J. Heat Transfer
0022-1481, 129
, pp. 835
–843
.29.
Vadasz
, P.
, 1998, “Coriolis Effect on Gravity-Driven Convection in a Rotating Porous Layer Heated From Below
,” J. Fluid Mech.
0022-1120, 376
, pp. 351
–375
.30.
Givler
, R. C.
, and Altobelli
, S. A.
, 1994, “A Determination of the Effective Viscosity for the Brinkman-Forchheimer Flow Model
,” J. Fluid Mech.
0022-1120, 258
, pp. 355
–370
.31.
Nayfeh
, A. H.
, 1981, Introduction to Perturbation Techniques
, Wiley-Interscience
, New York
.32.
Malkus
, W. V. R.
, and Veronis
, G.
, 1958, “Finite Amplitude Cellular Convection
,” J. Fluid Mech.
0022-1120, 4
(3
), pp. 225
–232
.33.
Chandrasekhar
, S.
, 1961, Hydrodynamic and Hydromagnetic Stability
, Oxford University Press
, London
.34.
Krishnamurti
, R. E.
, 1967, Ph.D. thesis, University of California, Los Angeles.35.
Veronis
, G.
, 1963, “Penetrative Convection
,” Astrophys. J.
0004-637X, 137
, pp. 641
–663
.Copyright © 2008
by American Society of Mechanical Engineers
You do not currently have access to this content.
