A note on the second problem of Stokes for Newtonian fluids

New and simpler exact solutions corresponding to the second problem of Stokes for Newtonian fluids are established by the Laplace transform method. These solutions, presented as a sum of the steady-state and transient solutions are in accordance with the previous results (see Figs. 1–4). The amplitudes of the wall shear stresses corresponding to the cosine and sine oscillations are almost identical, except for a small initial time interval. The time required to attain the steady-state for the cosine oscillations of the boundary is smaller than that for the sine oscillations of the boundary. This time decreases if the frequency of the velocity of the boundary increases.