General formulation and solution of Navier-Stokes and energy equations are sought in the study of threedimensional axisymmetric unsteady stagnation-point flow and heat transfer impinging on a flat plate when the plate is moving with variable velocity and acceleration towards the main stream or away from it. As an application, among others, this accelerated plate can be assumed as a solidification front which is being formed with variable velocity. An external fluid, along z - direction, with strain rate a impinges on this flat plate and produces an unsteady three-dimensional axisymmetric flow in which the plate moves along z - direction with variable velocity and acceleration in general. A reduction of Navier-Stokes and energy equations is obtained by use of appropriate similarity transformations, for the first time. The obtained ordinary differential equations are solved by using finite-difference numerical techniques. Velocity and pressure profiles along with temperature profiles are presented for different examples of the plate velocity functions and selected Prandtl numbers. According to the results obtained, the velocity and thermal boundary layers feel the effect of variations of the plate velocity more than the plate acceleration. It means that the minimum boundary layer thickness happens at the maximum value of the plate velocity and acceleration effect plays a secondary role.

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