| dc.description.abstract |
In this work, problems dealing with unsteady unidirectional flows of a Maxwell fluid in
a porous medium are investigated. By using modified Darcys law of a Maxwell fluid,
the equations governing the flow are modeled. Employing Sumudu transform, the an-
alytic solutions of the modeled equations are developed for the following problems:(i)
unsteady Couette flow, (ii) unsteady flow for rigid and free boundaries, (iii) flow
between two parallel plates suddenly set in motion with same speed, (iv) unsteady
Poiseuille flow, (v) unsteady generalized Couette flow and (vi) unsteady generalized
Couette flow for rigid and free boundaries. Since the Sumudu transform has units
preserving properties, therefore aforementioned problems are solved without restoring
the frequency domain. But these properties not exist in the Laplace transform, which
is the major benefit of Sumudu transform over the Laplace transform. Further, the
solutions for the velocity fields that have been obtained, have complete agreement
with those established by using the Laplace transform. Moreover, the corresponding
solutions for Newtonian fluids as well as those for Maxwell fluids are obtained as
limiting cases of our solutions. Finally, the influence of the pertinent parameters on
the velocity of fluids is also analyzed by graphical illustrations. |
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