The University of British Columbia

{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