Department of Mathematics

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Analytical solutions for unsteady flow problems of Maxwell fluid in a porous mediam
(Science International, 2015) Siddique; Abdullah Y. Al Hossain; M. B. Riaz
In this paper, the problems of unsteady unidirectional flow of Maxwell fluid in a porous media are examined. The governing equations of flow are modelled, by employing the modified Darcy's law of a Maxwell fluid. Using Sumudu transform, analytical solutions of modelled equations are established for the following problems: (i) unsteady Couette flow, (ii) unsteady Poiseuille flow and (iii) unsteady generalized Couette flow. Since the Sumudu transform has units preserving properties, therefore aforementioned problems are solved without restoring the frequency domain. This is one of many strength points for this new transform, especially with respect to applications in problems with physical dimensions. 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 can be obtained as limiting cases of our solutions. Finally, the impact of relevant parameters on the velocity of fluids is also analyzed by graphical illustrations.