Abstract
This work deals with finding exact solution of the Stokes' problem analogue to a composite free flow and porous matrix layers. The upper free flow region is bounded above by a plate moving with a time dependent velocity and the bottom porous layer is of unbounded depth. The velocity field corresponding to this Stokes' problem is obtained by means of Laplace transform, Mellin-Fourier transform and Faltung theorem on convolution. This study investigates the effect of the transition zone (mushy layer) length on the interfacial velocity profile. We have compared these results with the classical Stokes' problem. We realize that the findings of this work are useful in understanding flow mechanics in solidification process of multi-component melts, the impact of viscous shearing inside the lumen region of an endothelial glycocalyx layer of human arteries.
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