Division of Mathematics, General Education Center, Chienkuo Technology University, Changhua City 500, Taiwan
Copyright © 2009 Chi-Min Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
A shear flow motivated by relatively moving half-planes is theoretically studied in
this paper. Either the mass influx or the mass efflux is allowed on the boundary. This
flow is called the extended Stokes' problems. Traditionally, exact solutions to the
Stokes' problems can be readily obtained by directly applying the integral transforms
to the momentum equation and the associated boundary and initial conditions.
However, it fails to solve the extended Stokes' problems by using the
integral-transform method only. The reason for this difficulty is that the inverse
transform cannot be reduced to a simpler form. To this end, several crucial
mathematical techniques have to be involved together with the integral transforms to
acquire the exact solutions. Moreover, new dimensionless parameters are defined to
describe the flow phenomena more clearly. On the basis of the exact solutions derived
in this paper, it is found that the mass influx on the boundary hastens the development
of the flow, and the mass efflux retards the energy transferred from the plate to the