An Exact Periodic Solution of a Hydromagnetic Flow in a Horizontal Channel

Abstract

An exact periodic solution for the hydromagnetic unsteady flow of an incompressible fluid with constant properties is obtained. The hydrodynamic (HD) and the hydromagnetic (HM) cases are studied. The flow field here is a generalization of the well-known Couette flow, in which one wall is at rest and the other wall oscillates in its own plane about a constant mean velocity. In order to have some suggestions about the approximate solutions, the exact solution is compared with its own approximate form.