Linear stability of a steady non-isothermal Couette flow between two cylinders for the case where the inner cylinder is rotating with constant angular velocity ω while the outer cylinder is at rest is investigated. The base velocity vector has two components: the azimuthal component due to rotation and the vertical component due to internal heat sources distributed within the fluid in accordance with the Arrhenius law. The base flow velocity and temperature satisfy a nonlinear boundary value problem which is solved numerically. Linearized equations for the perturbed quantities are solved by means of the collocation method based on the Chebyshev polynomials. Numerical results show that the increase in ω destabilizes the flow. Thus, rotation can be considered as one of the factors that enhances instability.

1.
P. G.
Drazin
and
W. H.
Reid
,
Hydrodynamic Stability
(
Cambridge University Press
,
Cambridge
,
2004
), ISBN 9780511616938.
2.
J. M.
Lopez
,
F.
Marques
, and
M.
Avila
(
2015
)
Conductive and convective heat transfer in fluid flows between differentially heated and rotating cylinders
,
International Journal of Heat and Mass Transfer
90
,
959
967
.
3.
U. A.
Al-Mubaiyedh
,
R.
Sureshkumar
, and
B.
Khomami
(
2002
)
The effect of viscous heating on the stability of Taylor-Couette flow
,
Journal of Fluid Mechanics
462
,
111
132
.
4.
H. N.
Yoshikawa
,
M.
Nagata
, and
I.
Mutabazi
(
2013
)
Instability of the vertical annular flow with a radial heating and rotating inner cylinder
,
Physics of Fluids
25
,
114104
.
5.
A. A.
Kolyshkin
and
R.
Vaillancourt
(
1993
)
On the stability of non-isothermal circular Couette flow
,
Physics of Fluids
5
,
3136
3146
.
6.
A. A.
Kolyshkin
and
R.
Vaillancourt
(
1996
)
Linear stability of Couette flow with rotating inner cylinder and radially nonuniform internal heat sources
,
International Journal of Heat and Mass Transfer
39
,
537
545
.
7.
I.
Barmina
,
M.
Purmalis
,
R.
Valdmanis
, and
M.
Zake
(
2016
)
Electrodynamic control of the combustion characteristics and heat energy production
,
Combustion Science and Technology
188
,
190
206
.
8.
M.
Abricka
,
I.
Barmina
,
R.
Valdmanis
,
M.
Zake
, and
H.
Kalis
(
2016
)
Experimental and numerical studies on integrated gasification and combustion of biomass
,
Chemical Engineering Transactions
50
,
127
132
.
9.
V.
Koliskina
,
A.
Kolyshkin
,
I.
Volodko
, and
H.
Kalis
, “On the stability of a convective motion generated by a chemically reacting fluid in a pipe,” in
Conference Proceedings
1738
, (
American Institute of Physics
,
Melville, NY
,
2016
).
10.
Y. B.
Zeldovich
,
G. I.
Barenblatt
,
V. B.
Librovich
, and
G. M.
Makhviladze
,
Mathematical Theory of Combustion and Explosions
(
Consultants Bureau
,
New York
,
1985
), ISBN 0306109743.
This content is only available via PDF.
You do not currently have access to this content.