A time dependent slip flow of a couple stress fluid between two parallel plates through state space

In this work, the time dependent flow of an incompressible couple stress fluid passing two infinite parallel plates is investigated. The fluid motion is generated by applying a constant pressure gradient together with a sudden motion of one of the two plates. The linear slip velocity and the vanishing couple stresses on the boundary are applied on both plates. A generalized solution is obtained analytically by utilizing the integral Laplace transform together with the state space technique in the Laplace domain. The inversion of Laplace transform is obtained numerically by using a standard numerical method adopted by Honig and Hirdes. The effects of couple stress viscosity coefficient and slip parameters on both plates are studied numerically. The results show that the increase in the couple stress and slip coefficients results in a decrease in the fluid velocity in the case of stationary plates. However the velocity of the fluid is amplified by the increase of these parameters when the upper plate is set in motion.