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On accelerated flows of an Oldroyd-B fluid in a porous medium. (English) Zbl 1154.76317
Summary: In this work, the problems dealing with unsteady unidirectional flows of an Oldroyd-B fluid in a porous medium are investigated. By using modified Darcy’s law of an Oldroyd-B fluid, the equations governing the flow are modelled. Employing Fourier sine transform, the analytic solutions of the modelled equations are developed for the following two problems: (i) constant accelerated flow, (ii) variable accelerated flow. Explicit expressions for the velocity field and adequate tangential stress are obtained in each case. The solutions for Newtonian, second grade and Maxwell fluids in a porous medium appear as the limiting cases of the present analysis.

76A10 Viscoelastic fluids
35Q35 PDEs in connection with fluid mechanics
76S05 Flows in porous media; filtration; seepage
Full Text: DOI
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