Start-Up of Pressure-Driven Flow between Two Flat Plates
Consider two flat plates a distance 2B apart. The fluid between the plates is quiescent, and then at time t = 0 a pressure gradient is applied to create a laminar, unidirectional flow parallel to the plates. We wish to determine the start-up of this flow and its eventual steady state.
What is the unsteady equation describing this flow and the initial and boundary conditions?