Similarity solution of unaxisymmetric heat transfer of an unsteady viscous flow in the vicinity of an axisymmetric stagnation point of an infinite circular cylinder with simultaneous axial and rotational movement along with transpiration $Uo$ is investigated when the angular velocity, axial velocity, and wall temperature or wall heat flux vary arbitrarily with time. The impinging free stream is steady and with a strain rate of $k¯$. The results presented are found by numerical integration. The local coefficient of heat transfer (Nusselt number) is found to be independent of time and place, though the cylinder wall temperature or wall heat flux are functions of both time and place.

1.
Gorla
,
R. S. R.
, 1977, “
Unsteady Laminar Axisymmetric Stagnation Flow Over a Circular Cylinder
,”
Dev. Mech.
0419-0262,
9
, pp.
286
288
.
2.
Gorla
,
R. S. R.
, 1978, “
Nonsimilar Axisymmetric Stagnation Flow on a Moving Cylinder
,”
Int. J. Eng. Sci.
0020-7225,
16
, pp.
397
400
.
3.
Gorla
,
R. S. R.
, 1978, “
Transient Response Behavior of an Axisymmetric: Stagnation Flow on a Circular Cylinder Due to Time Dependent Free Stream Velocity
,”
Int. J. Eng. Sci.
0020-7225,
16
, pp.
493
502
.
4.
Gorla
,
R. S. R.
, 1979, “
Unsteady Viscous Flow in the Vicinity of an Axisymmetric Stagnation-Point on a Cylinder
,”
Int. J. Eng. Sci.
0020-7225,
17
, pp.
87
93
.
5.
Gorla
,
R. S. R.
, 1976, “
Heat Transfer in an Axisymmetric Stagnation Flow on a Cylinder
,”
Appl. Sci. Res.
0003-6994,
32
, pp.
541
553
.
6.
Cunning
,
G. M.
,
Davis
,
A. M. J.
, and
Weidman
,
P. D.
, 1998, “
Radial Stagnation Flow on a Rotating Cylinder With Uniform Transpiration
,”
J. Eng. Math.
0022-0833,
33
, pp.
113
128
.
7.
Saleh
,
R.
, and
Rahimi
,
A. B.
, 2004, “
Axisymmetric Stagnation-Point Flow and Heat Transfer of a Viscous Fluid on a Moving Cylinder With Time-Dependent Axial Velocity and Uniform Transpiration
,”
ASME J. Fluids Eng.
0098-2202,
126
, pp.
997
1005
.
8.
Rahimi
,
A. B.
, and
Saleh
,
R.
, 2007, “
Axisymmetric Stagnation-Point Flow and Heat Transfer of a Viscous Fluid on a Rotating Cylinder With Time-Dependent Velocity and Uniform Transpiration
,”
ASME J. Fluids Eng.
0098-2202,
129
, pp.
106
115
.
9.
Press
,
W. H.
,
Flannery
,
B. P.
,
Teukolsky
,
S. A.
, and
Vetterling
,
W. T.
, 1997,
Numerical Recipes: The Art of Scientific Computing
,
Cambridge University Press
,
Cambridge
.