Similarity solutions of axisymmetric stagnation-point flow and heat transfer of a viscous, Boussinesq-related density fluid on a moving flat plate

The problem of unsteady three-dimensional axisymmetric stagnation-point flow and heat transfer of a viscous compressible fluid on a flat plate is solved 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 the use of suitably-introduced similarity transformations. The temperature of the plate wall is kept constant which is different with that of the main 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 (beta), wall temperature, Prandtl number and plate velocity at both steady and unsteady cases. According to the results obtained, it is revealed that when the plate moves away from the impinging flow, thermal and velocity boundary layer thicknesses get higher values compared to the plate moving upward. Besides, it is captured that the value of beta and Pr number do not have any significant effect on shear stress and, also, heat transfer for a plate moving away from the incoming potential flow. (C) 2014 Sharif University of Technology. All rights reserved.