A linear stability analysis of Rayleigh-Be´nard-Marangoni flow of low Prandtl number fluid contained in an open vertical cylinder is presented. The cylinder is heated laterally and is cooled at top surface by radiation. Governing equations of the flow are solved for axisymmetric base flow using higher order finite difference scheme. Small perturbation was applied to the obtained base flow to determine the critical Marangoni number and Grashof number at which the axisymmetry is broken. The eigenvalue matrix equation is solved using linear fractional transformation with banded matrix structure taken into account. It is found that the thermocapillary effect stabilizes the convective flow driven by buoyancy.

1.
Hurle
D. T. J.
,
Temperature oscillations in molten metals and their relationship to growth striae in melt-grown crystal
,
Philos. Mag.
Vol.
13
,
305
305
,
1966
.
2.
Chandrasekhar, S., Hydrodynamic and Hydromagnetic Stability, Oxford University Press, New York, 1961.
3.
Charlson
G. S.
and
Sani
R. L.
,
Thermaconvective instability in a bounder cylindrical fluid layer
,
Int. J. Heat Mass Transf.
, Vol.
13
,
1479
1479
,
1970
4.
Charlson
G. S.
and
Sani
R. L.
,
On thermaconvective instability in a bounder cylindrical fluid layer
,
Int. J. Heat Mass Transf.
, Vol.
14
,
2157
2157
,
1970
5.
Stork
K.
and
Mu¨ller
,
Convection in boxes: An experimental investigation in vertical cylinder and annuli
,
J. Fluid Mechanics
, Vol.
71
,
231
231
,
1975
.
6.
Rosenblat
S.
,
Thermal convection in a vertical cylinder
,
J. Fluid Mechanics
, Vol.
122
,
395
395
,
1982
.
7.
Buell
J. C.
and
Catton
I.
,
The effect of wall conduction on the stability of a fluid in a right circular cylinder heated from below
,
J. Heat Transfer
, Vol.
105
,
255
255
,
1983
.
8.
Neumann
G
,
Three-dimensinal numerical simulation of buoyancy-driven convection in vertical cylinders heated from below
,
J. Fluid Mechanics
, Vol.
214
,
559
559
,
1990
.
9.
Wanschura
M.
,
Kuhlmann
H. C.
and
Rath
H. J.
,
Three-dimensional instability of axisymmetric buoyant convection in cylinder heated from below
,
J. Fluid Mechanics
, Vol.
326
,
339
339
,
1996
.
10.
Pearson
J. R. A.
,
On convection cells induced by surface tension
,
J. Fluid Mechanics
, Vol.
4
,
489
489
,
1958
.
11.
Vrentas
J. S.
,
Narayanan
R.
and
Agrawal
S. S.
,
Free surface convection in bounded cylindrical geometry
,
Int. J. Heat Mass Transf.
, Vol.
24
,
9
,
1513
1513
,
1981
.
12.
Dauby
P. C.
,
Lebon
G.
and
Bouhy
E.
,
Linear Be´nard-Marangoni instability in rigid circular containers
,
Phys. Review E
, Vol.
56
,
1
,
520
520
,
1997
.
13.
Jing
C. J.
,
Imaishi
N.
,
Yasuhiro
S.
, and
Miyazawa
Y.
,
Three-dimensional numerical simulation of spoke pattern in oxide melt
,
J. Crystal Growth
, Vol.
200
,
204
204
,
1999
.
14.
Ai, X. and Li, B. Q., Stability of magnetically-driven flows in levitated droplets, Proceedings of IMECE, Paper No. 33276, 2002.
This content is only available via PDF.
You do not currently have access to this content.