Energetic balance for the flow of a second-grade fluid due to a plate subject to a shear stress

Exact and approximative expressions for dissipation, the power due to the shear stress at the wall and the boundary layer thickness corresponding to the unsteady motion of a second-grade fluid, induced by an infinite plate subject to a shear stress, are established. For α1 0, similar results for Newtonian fluids performing the same motion are obtained. The results that have been obtained here are different to those corresponding to the Rayleigh–Stokes problem. A series solution for the velocity field is also determined. Its form, as was to be expected, is identical to that resulting from the general solution using asymptotic approximations.