Some effects of side walls on unsteady flow of a viscous fluid over a plane wall

Four types of unsteady flows of a viscous fluid over a plane wall bounded by two side walls are considered. They are flow caused by impulsive motion of a plate, flow due to oscillation of a plate, flow induced by constantly accelerating plate, and flow imposed by a plate that applies a constant tangential stress to the fluid. In order to solve these problems, the sine and cosine transformations are used, and exact solutions for the velocity distribution are found in terms of definite integrals. The cases for which the time goes to infinity and the distance between two side walls goes to infinity are compared with the cases for flows over a plane wall in the absence of the side walls. These provide to know the required time to attain the steady-state and what is the distance between the side walls for which the measured value of the velocity or the stress would be unaffected by the presence of the side walls.