Extended Stokes' Problems for Relatively Moving Porous Half-Planes

A shear flow motivated by relatively moving half-planes is theoretically studied inthis paper. Either the mass influx or the mass efflux is allowed on the boundary. Thisflow is called the extended Stokes' problems. Traditionally, exact solutions to theStokes' problems can be readily obtained by directly applying the integral transformsto the momentum equation and the associated boundary and initial conditions.However, it fails to solve the extended Stokes' problems by using theintegral-transform method only. The reason for this difficulty is that the inversetransform cannot be reduced to a simpler form. To this end, several crucialmathematical techniques have to be involved together with the integral transforms toacquire the exact solutions. Moreover, new dimensionless parameters are defined todescribe the flow phenomena more clearly. On the basis of the exact solutions derivedin this paper, it is found that the mass influx on the boundary hastens the developmentof the flow, and the mass efflux retards the energy transferred from the plate to thefar-field fluid