A perturbation technique is used to obtain analytically the velocity and temperature oscillations in a laminar free convection boundary layer on a plane wall vibrating transversely. The problem is divided into high and low values of $ω4x$ where ω and x are, respectively, the dimensionless frequency and distance from the leading edge. Solutions are compared by plotting the oscillating components of the wall shear stress and temperature gradient. Results in the intermediate region of $ω4x$ are estimated by extrapolation of the solutions obtained for each limiting region.

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