Magnetohydrodynamic flow of non-Newtonian visco-elastic fluid through a porous medium near an accelerated plate

Abstract

An exact solution is obtained for the unsteady flow of an electrically conducting visco-elastic incompressible fluid through a porous medium on an infinite flat plate. The fluid under consideration obeys the rheological equations of state due to the Walters stress-strain relation. The plate is accelerated in the presence of a uniform magnetic field. The analysis includes the case of a solid plate as well as a porous one. The solution of the equations of motion is obtained by the use of a Laplace transform. The effects of the elasticity, magnetic field, permeability of the porous medium, and the suction of the plate on the velocity distribution, as well as on skin friction, are discussed. The analytical results are confirmed numerically. It is found that the velocity distribution increases with an increase of both elasticity and permeability, while it decreases as the magnetic parameter increases. It is also found that the skin friction decreases with an increase in the magnetic field and elasticity parameters, while it increases with an increase of both the permeability of the porous medium and the suction of the plate. PACS Nos.: 47.50.+d, 47.55.Mh, 47.85.Dh Résumé : Nous obtenons une solution exacte pour le problème de l'écoulement instable d'un fluide conducteur, viscoélastique et incompressible à travers un milieu poreux sur une surface plane infinie. Ce fluide obéit aux équations d'état rhéologiques dues à la relation effort-déformation de Walters. La plaque est accélérée et un champ magnétique est présent.L'analyse inclut aussi bien une plaque solide que poreuse. La solution des équations de mouvement est obtenue par transformation de Laplace. Nous analysons les effets de l'élasticité, du champ magnétique, de la perméabilité du milieu poreux et de la succion de la plaque sur la distribution de vitesse et sur la friction de surface. Les résultats analytiques sont confirmés par calcul numérique. Nous trouvons que la distribution de vitesse augmente avec l'élasticité et la perméabilité et décroît lorsque le champ magnétique croît. Nous trouvons aussi que la friction de surface diminue lorsque le champ magnétique et les paramètres d'élasticité augmentent.[Traduit par la Rédaction]

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