The laminar free-convection boundary layer on a vertical plane wall vibrating transversely at high frequencies is analyzed utilizing a perturbation technique. The zeroth-order solutions are that of the well-known steady free-convection flow. First-order harmonic oscillations in velocity and temperature and a second-order time-independent secondary flow and heat transfer are obtained. Series solution for shear stress and Nusselt number are presented having both time-dependent and time-independent terms. Prandtl numbers of 0.72 and 10 are investigated. The time-independent or steady Nusselt number was found to decrease while the shear stress was found to increase under the influence of oscillations.

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