The paper analyses the effect of concentration modulation at the onset of solute magneto-convection and heat transfer in a weak electrically conducting fluid by carrying out a linear and non-linear analysis. The Venezian approach is assented encompassing the correction Solute Rayleigh number and wave numbers for meagre amplitude concentration modulation. A multiscale method is applied to convert the analytically untraceable Lorenz model to an analytically traceable Ginzburg-Landau equation which is solved to quantify mass transfer through Sherwood number. It is observed that concentration modulation results in sub-critical motion however out-of-phase concentration modulation is more stable compare to others.
REFERENCES
1.
A.C.
Eringen
, “Simple Microfluids
”, Int. J. Eng. Sci.
, 2
(2
), pp. 205
–217
, 1964
.2.
3.
G.
Ahmadi
, “Stability of Micropolar Fluid Layer Heated from Below
”, Int. J. Eng. Sci.
, 14
, pp. 81
–85
, 1976
.4.
G.
Lukasazewicz
, “Micropolar Fluid-Theory and Applications”, Birkhausr
, Bostan
, 1999
.5.
B.
Datta
and V. U. K.
Sastry
, “Thermal Instability of a Horizontal layer of Micropolar Fluid Heated from Below
”, Int. J. Eng. Sci.
, 14
(7
), pp. 631
–637
, 1976
.6.
S.P.
Battacharyya
and S.K.
Jena
, “On the stability of a hot layer of micropolar fluid
”, Int. J. Eng.
, 21
(9
), pp. 1019
–1024
, 1983
.7.
P.G.
Siddheshwar
and S.
Pranesh
, “Linear and weakly non-linear analyses of convection in a micropolar uid
”, Hydrodyanamics theory and Applicat.
, pp. 489
–493
, 2005
.8.
Bhadauria
B.S
, “Time-periodic heating of Rayleigh-Benard convection in a vertical Magnetic field
”, Physica Scripta
, 73
, pp. 296
–302
, 2006
.9.
S.
Pranesh
and Sangeetha
George
, “Effect of Magnetic Field on the onset of Rayleigh Benard convection in Boussinesq Stoke Suspensions with time periodic boundary temperatures
”, Int. J. App. Math. Mech.
, 6
(16
), pp. 38
–55
, 2011
.10.
S.
Pranesh
, “The Effect Of Imposed Time-Periodic Boundary Temperature And Electric Field on the onset of Rayleigh-Benard Convection in a Micropolar Fluid
”, Int. J. Eng. Rese. Tech.
, 2
(7
), pp. 734
–754
, 2013
.11.
P.G.
Siddheshwar
and S.
Pranesh
, “Effects of temperature/gravity modulation on the onset of magneto-convection in electrically conducting fluids with internal angular momentum
”, J. Magnetism and Magnetic Materials
, 6
(2
), pp. 104
–114
, 2002
.12.
P. G.
Siddheshwar
and S.
Pranesh
, “Magnetoconvection in fluids with suspended particles under 1g and µg
”, Aer. Sci. Tech.
, 6
(2
), pp. 105
–114
, 2002
.13.
P.G.
Siddheshwar
and S.
Pranesh
, “Magnetoconvection in a micropolar fluid
”, Int. J. Eng. Sci.
, 36
, pp. 1173
–1181
, 1998
.14.
R. J.
Donnelly
, “Experiments on the stability of viscous flow between rotating cylinders. III Enhancement of stability by modulation
”, Proc. Roy. Soc. Lond. A.
, pp. 130
–139
, 1964
.15.
G.
Venezian
, “Effect of modulation on the onset of thermal convection
”, J. Fluid Mech.
, 5
(3
), pp. 243
–254
, 1969
.16.
Rosenblat
S.
and Tanaka
G.A
, “Modulation of thermal convection instability
”, Physics of Fluids
, 14
, pp. 1319
–1322
, 1971
.17.
Roppo
M.H
, Davis
S.H
, Rosenblat
S
, “Benard convection with time periodic heating
”, Physics of Fluids
, 27
, pp. 796
–803
, 1984
.18.
P. G.
Siddheshwar
and S.
Pranesh
, “Effect of a non-uniform basic temperature gradient on Rayleigh-Benard convection in a micropolar fluid
”, Int. J. Eng. Sci.
, 36
(11
), pp. 1183
–1196
, 1998
.19.
Bhadauria
B.S
, “Time-periodic heating of Rayleigh-Benard convection in a vertical Magnetic field
”, Physica Scripta
, 73
, pp. 296
–302
, 2006
.20.
S.
Pranesh
and Sangeetha
George
, “Effect of imposed time periodic gravity modulation and electric field on the onset of Rayleigh-Benard convection in a couple stress fluid
”, Int. J. Math. Sci. Eng. App.
, 6
(6
), pp. 421
–435
, 2012
.21.
B.S.
Bhaduria
, P.G.
Siddheshwar
and Ishak
Hashim
, “Effects of Time-Periodic Thermal Boundary Conditions and Internal Heating on Heat Transport in a Porous Medium
”, Transport in porous media
, 97
(2
), pp. 185
–200
, 2013
.22.
S.
Pranesh
and Sameena
Tarannum
, “Linear and Weakly Non-Linear Stability Analyses of Double- Diffusive Electro-Convection in a Micropolar Fluid
”, IOSR J. Math.
, pp. 44
–70
, 2015
.23.
T. V.
Joseph
, S.
Pranesh
and S.
Manjunath
, “Linear and Non-linear analysis of electrothermo convection in a micropolar fl uid
”, J. Heat and Mass Transfer
, 14
(4
), pp. 461
–484
, 2017
.24.
Wheeler
, G.B.
MsFadden
, T.B.
Murray
, S.R.
Coriell
and Saunders
B.V
, “The effects of gravity modulation on thermosolutal convection in an infinite layer of fluid
”, Phys. Fluids A
, 4
(6
), pp. 1176
–1189
, 1992
.25.
G.
Veronis
, “Cellular convection with finite amplitude in a rotating fluid
”, J. Fluid Mech.
, 5
, 401
–35
, 1959
.
This content is only available via PDF.
© 2019 Author(s).
2019
Author(s)
You do not currently have access to this content.