Axisymmetric stagnation-point flow and heat transfer of a viscous fluid on a moving plate with time-dependent axial velocity and uniform transpiration

The unsteady viscous flow and heat transfer in the vicinity of an axisymmetric stagnation pointof an infinite moving plate with transpiration w0 are investigated when the axial velocity and wall temperaturevary arbitrarily with time. the free stream is steady and with a strain rate of a. an exact solutionof the navierstokes equations and energy equation is derived in this problem. a reduction of theseequations is obtained by the use of appropriate transformations for the most general case when the transpirationrate is also time-dependent, but results are presented only for uniform values of this quantity.the general self-similar solution is obtained when the axial velocity of the plate and its wall temperaturevary as specified time-dependent functions. for completeness, sample semi-similar solutions of theunsteady navierstokes equations have been obtained numerically using a finite difference scheme. allthe solutions above are presented for different values of dimensionless transpiration rate, s d w0=pa,where  is the kinematic viscosity of the fluid. the effects of the sundry parameters, including transpirationrate, prandtl number, oscillation frequency and accelerating/decelerating parameter, on the velocityand temperature profiles, as well as surface shear stresses and heat transfer coefficient, are investigatedand results are shown through graphs.