Unsteady boundary layer flow in the region of the stagnation point on a stretching sheet

Unsteady two-dimensional stagnation point flow of an incompressible viscous fluid over a flat deformable sheet is studied when the flow is started impulsively from rest and the sheet is suddenly stretched in its own plane with a velocity proportional to the distance from the stagnation point. After a similarity transformation, the unsteady boundary layer equation is solved numerically using the Keller-box method for the whole transient from tau = 0 to the steady state tau --> infinity. Also, a complete analysis is made of the governing equation at tau = 0, the initial unsteady flow, at large times tau = infinity, the steady state flow, and a series solution valid at small times tau (much less than1). It is found that there is a smooth transition from the initial unsteady state flow (small time solution) to the final steady state flow (large time solution). (C) 2004 Elsevier Ltd. All rights reserved.