The problem of unsteady three-dimensional axisymmetric stagnation-point flow and heat transfer of a viscous compressible fluid on a flat plate is intended to solve when the plate can move with any arbitrary time-dependently variable or constant velocity. An external low Mach number potential flow impinges, along z-direction, on the flat plate with strain rate a to produce three-dimensional axisymmetric stagnation-point flow where the plate moves toward or away from impinging flow, concurrently. An exact solution of the governing Navier-Stokes and energy equations is obtained by use of suitably-introduced similarity transformations. The temperature of the plate wall is kept constant which is different with of the main stream. The density of the fluid changes because of the temperature difference between the wall and free stream. A Boussinesq approximation is used to take into account the density variations of the fluid. The results are presented for a wide range of parameters characterizing the problem including volumetric expansion coefficient (β), wall temperature, Prandtl number and plate velocity at both steady and unsteady cases. According to the results obtained, it is revealed, for fixed characterizing parameters, that when the plate moves away from the impinging flow, thermal and velocity boundary layer thicknesses get considerable higher values compared to the plate moving upward. Besides, it is captured that the value of β and Pr numbers does not have any significant effect on shear stress and, also, heat transfer coefficient for a plate moving away from the incoming potential flow.

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