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Velocity Field Between Two Plates: 1 Fixed, 1 Moving with Sinusoidal Motion u=Asin(omega*t)

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Two infinite parallel plates are separated by a distance h. The space between them is filled with a Newtonian fluid: density (rho), viscosity (mu). The lower plate is fixed, but the upper plate executes a sinusoidal motion. (U=A*sin(omego*t). Calculate the velocity field between the plates, and plot some representative profiles.

coordinates x-dir along plate
y-dir normal to plate.

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Solution Summary

This full solution uses the only non-degenerated equation of motion p*(partial derivative u)/(partial derivative t) = u*(partial derivative^2*u)/(partial derivative y^2) and introducing non dimensional variables u' = u/A.

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