A study of internal heat generationeffect with gravity modulationin a horizontal layer of magnetic nanofluidin the occurrence of evenvertical magnetic field on the onset of Benard-Marangoni convection heated from below is presented. Theupper boundary, which is free, considered flat and undeformable and thelower boundary is assumed to be rigid. Upper and lower boundaries are insulated perfectly to temperature perturbations. Galerkintechnique is used to solve numerically eigenvalue problem. It is inferred that the internal heat source strength and gravity modulation has considerable influence on the onset of convection.

1.
R.E.
Rosensweig
,
Ferrohydrodynamics
,
Cambridge University Press
,
New York
(
1985
).
2.
V. G.
Bashtovoy
,
B. M.
Berkovsky
,
A. N.
Vislovich
,
Introduction to Thermo mechanics of Magnetic fluid
,
Hemisphere
,
Washington
(
1988
).
3.
V. G.
Bashtovoy
,
B. M.
Berkovsky
,
A. N.
Vislovich
,
Magnetic Fluids Engineering Applications
,
Oxford University Press
,
Oxford
(
1993
).
4.
B. A.
Finlayson
,
Convective instability of ferro magnetic fluids
,
J. Fluid Mech
,
40
,
753
767
(
1970
).
5.
D. P.
Lalas
,
S.
Carmi
,
Thermo convective stability of ferro fluids
,
Phys. Fluids
4
,
436
437
(
1971
).
6.
M. I.
Shliomis
,
Magnetic fluids
.
Soviet Phys. Uspekhi (Engl. Trans)
17
,
153
169
(
1974
).
7.
K.
Gotoh
,
M.
Yamada
,
Thermal convection in a horizontal layer of magnetic fluids
,
J. Phys. Soc. Japan
,
51
,
3042
3048
(
1982
).
8.
P.J.
Stiles
,
M.
Kagan
,
Thermo convective instability of a ferrofluid in a strong magnetic field
,
J. Colloid Interface Sci
,
134
,
435
448
(
1990
).
9.
P. N.
Kaloni
,
J. X.
Lou
,
Convective instability of magnetic fluids under alternating magnetic fields
,
Physical Review E
,
70
,
0663113
026324
(
2004
).
10.
S.
Odenbach
,
Recentprogress in magneticfluidresearch
,
Journal of PhysicsCondens. Matter
,
16
,
1135
1150
(
2004
).
11.
C. E.
Nanjundappa
,
I. S.
Shivakumara
,
R.
Arunkumar
,
Rafeal Tadmor, Ferroconvection in a porous medium with vertical throughflow
,
Acta Mechanica
,
226
,
1515
1528
(
2014
).
12.
R.
Arunkumar
,
C. E.
Nanjundappa
,
I. S.
Shivakumara
,
Effect of Cubic Temperature Profiles on Ferro Convection in a BrinkmanPorous Medium
,
Journal of Applied Fluid Mechanics
,
9
(
4
),
1955
1962
(
2016
).
13.
C. E.
Nanjundappa
,
I. S.
Shivakumara
,
R.
Arunkumar
,
Benard Marangoni ferroconvection with magnetic field dependent viscosity
,
J. Magn. Magn. Mater
,
322
(
15
),
2256
2263
(
2010
).
14.
C. E.
Nanjundappa
,
I. S.
Shivakumara
,
R.
Arunkumar
,
Onset of Marangoni-Benard Ferroconvection with Temperature Dependent Viscosity
,
Microgravity Sci. Technol
,
25
(
2
),
103
112
(
2013
).
15.
C. E.
Nanjundappa
,
I. S.
Shivakumara
,
R.
Arunkumar
,
Onset of Benard-Marangoni Ferroconvection with Internal Heat Generation
,
Microgravity Sci. Technol
,
23
(
1
),
29
39
(
2011
).
16.
H.
Nagarathnamma
,
A.
Pavithra
,
C. E.
Nanjundappa
,
S.P.
Suma
,
Penetrative Benard-Marangoni Convection in a Micro polar Ferro fluid Layer via Internal Heating and Submitted to a Robin Thermal Boundary Conditions
,
J. Elecromagnetic Analysis and applications
,
10
(
5
), (
2018
). DOI:
17.
R.
Arunkumar
,
Kavyashree
,
Linear stability analysis of ferro magnetic convection in presence of vertical throughflow
,
Materials Today : Proceedings
, , (
2020
).
18.
Brian
Straughan
,
Convection in a Variable Gravity Field
,
J. Mathematical Analysis and Applications
,
140
,
467475
(
1989
).
19.
J. Raymond Lee
Skarda
,
Insteability of a gravity modulated fluid layer with surface tension variations
,
J. Fluid Mech.
,
434
,
243
271
(
2001
).
20.
Vasudha
Yekasi
,
S.
Pranesh
,
Shahnaz
Bathul
,
Effects of Gravity Modulation and Internal Heat Generation on the onset of Rayleigh-Bénard convection in a Micropolar Fluid
,
J. advances in Mathematics
,
12
(
6
),
6270
6285
(
2016
).
21.
Amit
Mahajan
,
Mahesh Kumar
Sharma
,
The onset of convection in a magnetic nanofluid layer with variable gravity effects
,
Applied Mathematics and Computation
,
339
,
622
635
(
2018
).
This content is only available via PDF.
You do not currently have access to this content.