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 di erent 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.