@article {Saleh2004Axisymmetric-st,
title = {Axisymmetric stagnation-point flow and heat transfer of a viscous fluid on a moving cylinder with time-dependent axial velocity and uniform transpiration},
journal = {Journal of Fluids Engineering-Transactions of the ASME},
volume = {126},
number = {6},
year = {2004},
month = {NOV},
pages = {997-1005},
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 moving cylinder with time-dependent axial velocity and with uniform normal transpiration U-0 are investigated. The impinging free stream is steady and with a constant strain rate L An exact solution of the Navier-Stokes equations and energy equation is derived in this problem. A reduction of these equations is obtained by use of appropriate transformations for the most general case when the transpiration rate is also time-dependent but results are resented only for uniform values of this quantity. The general self-similar solution is obtained when the axial velocity of the cylinder and its wall. temperature or its wall heat flux vary as specified time-dependent functions. In particular the cylinder may move with constant speed, with exponentially increasing-decreasing axial velocity, with harmonically varying axial speed, or with accelerating-decelerating oscillatory axial 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 semisimilar solutions of the unsteady Navier-Stokes and energy equations have been obtained numerically using a finite-difference scheme. Some of these solutions are presented for special cases when the time-dependent axial velocity of the cylinder is a step-function, and a ramp function. All the solutions above are presented for Reynolds numbers},
keywords = {exact solution, stagnation flow, time-dependent axial movement, time-dependent heat transfer, transpiration},
issn = {0098-2202},
doi = {10.1115/1.1845556},
url = {http://dx.doi.org/10.1115/1.1845556\%7D},
author = {Saleh, R. and Rahimi, A. B.}
}