Exact solutions for three fundamental unsteady flows of an incompressible couple stress fluid between two parallel plates, namely, Couette, generalized Couette and Poiseuille flows, are obtained. Analytical solutions of the corresponding initial-boundary value problems are obtained by means of the integral transforms method (Laplace and finite sine Fourier transforms). For each flow type, the solution is written as the sum between the post transient solution (steady-state solution) and the transient solution. The volume flow rate and skin friction coefficients are, also, obtained. The effect of various parameters on the fluid velocity is graphically underlined and discussed and the critical time to reach the steady-state is also determined.
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Akhtar et al. (2016) studied this question.