@article {Rahimi2007Axisymmetric-st,
title = {Axisymmetric stagnation - Point flow and heat transfer of a viscous fluid on a rotating cylinder with time-dependent angular velocity and uniform transpiration},
journal = {Journal of Fluids Engineering-Transactions of the ASME},
volume = {129},
number = {1},
year = {2007},
month = {JAN},
pages = {106-115},
publisher = {ASME-AMER SOC MECHANICAL ENG},
type = {Article},
address = {THREE PARK AVE, NEW YORK, NY 10016-5990 USA},
abstract = {{The unsteady viscous flow and heat transfer in the vicinity of an axisymmetric stagnation point of an infinite rotating circular cylinder with transpiration U-0 are investigated when the angular velocity and wall temperature or wall heat flux all vary arbitrarily with time. The free stream is steady and with a strain rate of Gamma. 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 but results are presented only for uniform values of this quantity. The general self-similar solution is obtained when the angular velocity of the cylinder and its wall temperature or its wall heat flux vary as specified time-dependent functions. In particular, the cylinder may rotate with constant speed, with exponentially increasing/decreasing angular velocity, with harmonically varying rotation speed, or with accelerating/decelerating oscillatory angular speed. For self-similar flow, the surface temperature or its surface heat flux must have the same types of behavior as the cylinder motion. For completeness, sample semi-similar solutions of the unsteady Navier-Stokes equations have been obtained numerically using a finite-difference scheme. Some of these solutions are presented for special cases when the time-dependent rotation velocity of the cylinder is, for example, a step-function. All the solutions above are presented for Reynolds numbers},
keywords = {exact solution, stagnation flow, time-dependent heat transfer, time-dependent rotation, transpiration},
issn = {0098-2202},
doi = {10.1115/1.2375132},
url = {http://dx.doi.org/10.1115/1.2375132\%7D},
author = {Rahimi, A. B. and Saleh, R.}
}