Unsteady axisymmetric stagnation-point flow of a viscous fluid on a cylinder

The unsteady viscous flow in the vicinity of an axisymmetric stagnation poi nt of an infinite circular cylinder is investigated when both the free stre am velocity and the velocity of the cylinder vary arbitrarily with time. Th e cylinder moves either in the same direction as that of the free stream or in the opposite direction. The flow is initially (t = 0) steady and then a t t > 0 it becomes unsteady. The semi-similar solution of the unsteady Navi er-Stokes equations has been obtained numerically using an implicit finite- difference scheme. Also the self-similar solution of the Navier-Stokes equa tions is obtained when the velocity of the cylinder and the free stream vel ocity vary inversely as a linear function of time. For small Reynolds numbe r, a closed form solution is obtained. When the Reynolds number tends to in finity, the Navier-Stokes equations reduce to those of the two-dimensional stagnation-point flow. The shear stresses corresponding to stationary and t he moving cylinder increase with the Reynolds number. The shear stresses in crease with time for the accelerating flow but decrease with increasing tim e for the decelerating flow. For the decelerating case flow reversal occurs in the velocity profiles after a certain instant of time. (C) 1999 Elsevie r Science Ltd. All rights reserved.