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Journal of Porous Media
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ISSN Imprimir: 1091-028X
ISSN En Línea: 1934-0508

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Journal of Porous Media

DOI: 10.1615/JPorMedia.v12.i9.80
pages 919-926

Exact Solutions for the Accelerated Flows of a Generalized Second-Grade Fluid between Two Sidewalls Perpendicular to the Plate

Masood Khan
Department of Mathematics, Quaid-i-Azam University, Islamabad 44000, Pakistan

SINOPSIS

This paper is concerned with the exact solutions for the accelerated flows of a generalized second-grade fluid through a porous medium with a fractional derivative model. The fractional calculus approach is taken into account in the constitutive relationship of a non-Newtonian fluid model. Two characteristic examples, which are flow due to a constantly accelerating plate and flow due to variable accelerating plate between two sidewalls perpendicular to the plate, are considered. Employing the Fourier sine transforms and the theory of the Laplace transform for fractional calculus, the exact solutions are obtained. The solutions for a second-grade fluid appear as the limiting cases of the presented solutions by setting β = 1. Furthermore, in the absence of sidewalls, all solutions that have been constructed reduce to the known solutions of second-grade and Newtonian fluids corresponding to the motion over an infinite flat plate.


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