Unaxisymmetric Heat Transfer in the Axisymmetric Stagnation-Point Flow of a Viscous Fluid on a Cylinder with Simultaneous Axial and Rotational Movement Along with Transpiration

The unaxisymmetric heat transfer of an unsteady viscous
ow, in the vicinity of an axisymmetric
stagnation-point of an innite 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
ux vary arbitrarily with time. The impinging free stream is steady and
with a strain rate of k. An exact solution of the Navier-Stokes equations and energy equation
is derived in this problem. A reduction of these equations is obtained by the use of appropriate
transformations for the most general case, when the transpiration rate is also time-dependent.
However, results are presented only for uniform values of this quantity. The general self-similar
solution of unsteady unaxisymmetric heat transfer is obtained, in which unaxisymmetry is due to
the sinusoidal variation of the temperature, with respect to the surface position of the rotating
cylinder, and unsteadiness is because of the sinusoidal variation of the temperature of each
point of the cylinder surface, with respect to time and, also the rotation of the cylinder. All
the solutions are presented for Reynolds numbers, Re = ka2=2, ranging from 0.1 to 10.0 for
dierent values of Prandtl number and selected values of the dimensionless transpiration rate,
S = U0=ka, where a is the cylinder radius and  is the kinematic viscosity of the
uid. The
local coecient of heat transfer (Nusselt number) is found to be independent of time and place,
though the cylinder wall temperature or wall heat
ux are both functions of time and place.