Exact solutions for the flow of a dipolar fluid on a suddenly accelerated flat plate

The Laplace transformation is used to determine the exact general solution for the unsteady and irrotational flow of an incompressible dipolar fluid set to motion by the acceleration of a flat plate from rest. The general solution is found for arbitrary values of the dipolar constants d and l. In particular, attention is focused on the case of sudden plate motion for which the velocity field, the displacement thickness, the boundary layer thickness, and the dipolar stress component Sigma(yyx) have been determined. Special cases of the dipolar constants are also considered. It is shown that for a special boundary value of Sigma(yyx), the velocity distribution becomes independent of time. In addition, some significant new results concerning steady flows are presented. Finally, results obtained are compared to the corresponding case for a viscous Newtonian fluid.