Unsteady Boundary Layers on Vibrating Spheres in a Uniform Stream

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Abstract
The influence of radial vibrations on forced convection from a sphere placed in a uniform stream of an incompressible fluid is studied mathematically. Consideration is given to first-order perturbations of the harmonic vibrations of the spherical surface for both high and low frequencies. Theoretical results are obtained by means of a Kármán-Pohlhausen method for velocity and temperature distributions, skin friction, heat-transfer rate and the shift in the separation point of the boundary layer. Numerical calculations are carried out for boundary-layer thickness and velocity profiles in the fluctuating boundary layer.