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The spatial development of localized disturbances generated by three-dimensional vibrating surface in the Blasius boundary layer at critical Reynolds numbers was investigated. The experimental study is shown that the large amplitude of three-dimensional surface vibration leads to the formation of two types of disturbances in the boundary layer: wave packets and longitudinal localized structures. Downstream development of the high frequency oscillations of the wave packets at the central frequency is consistent with the linear theory of hydrodynamic stability. [ABSTRACT FROM AUTHOR]

The present study is performed to find the similarity solution like Blasius solution and also analyzed the effect of various dimensionless parameters on the momentum, thermal and nanoparticle concentration. In this respect we have considered the magnetohydrodynamic (MHD) unsteady boundary layer nanofluid flow and heat -- mass transfer along a porous stretching surface. So the governing partial differential equations are transformed to ordinary differential equations by using similarity transformations. The numerical solution is taken by applying the Nachtsgeim-Swigert shooting iteration technique along with Runge-Kutta integration scheme. The effects of various dimensionless parameters on velocity, temperature and nanoparticle concentration are discussed numerically and shown graphically. Therefore, from the figures it is observed that the results of velocity profile increases for increasing values of unsteadiness parameter, permeability parameter and stretching ratio parameter but there is no effect for magnetic parameter, the temperature profile decreases for increasing values of Brownian motion, unsteadiness, thermophoresis and stretching ratio but increases for magnetic parameter, the nanoparticle concentration decreases for increasing values of unsteadiness parameter, thermophoresis parameter, suction parameter, stretching ratio parameter and Lewis number but increases for magnetic parameter and Brownian motion parameter. For validity and accuracy the present results are compared with previously published work and found to in good agreement. [ABSTRACT FROM AUTHOR]

The paper presents a novel method that allows one to establish solutions of some non-linear ordinary differential equations, which contain products of the unknown functions and/or its derivatives. This method can be especially useful when one needs to address the problem of the solution existence for such equations. In particular' the method was used in this work for illustrative purposes' to find some solutions to the Blasius equation. [ABSTRACT FROM AUTHOR]