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Journal of Porous Media
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ISSN Imprimer: 1091-028X
ISSN En ligne: 1934-0508

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Journal of Porous Media

DOI: 10.1615/JPorMedia.v16.i9.20
pages 795-809

CLOSED-FORM SOLUTIONS FOR UNSTEADY MAGNETOHYDRODYNAMIC FLOWIN A POROUS MEDIUM WITH WALL TRANSPIRATION

Mohammed Abdulhameed
Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia 81310, Skudai, Malaysia
Ilyas Khan
Ton Duc Thang University
Arshad Khan
Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia 81310, Skudai, Malaysia; Department of Computer Science/IT Sarhad University of Science & IT, Peshawar Khyber Pakhtunkhwa Pakistan
Sharidan Shafie
Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia 81310 UTM Johor Bahru, Johor, Malaysia

RÉSUMÉ

This problem deals with an unsteady two-dimensional magnetohydrodynamic flow of incompressible viscous fluid over a flat plate with wall transpiration embedded in a porous medium. Exact solutions corresponding to the Stokes first and second problems are obtained using an extended separation of variable technique together with the similarity arguments. The corresponding starting solutions are presented as the sum of steady state and transient solutions. Further, it is found that for small time t the difference between the steady state and the transient solutions is significant. However, for large values of t, both of these solutions become identical. These solutions do not involve any unevaluated integral and are expressed in terms of exponential and complementary error functions. Effects of the material parameters on the velocity fields are investigated by plotting the graphs. The nature of the wall shear stress engendered due to the flow is also studied by presenting the results in graphical and tabular forms. Some well-known and fundamental solutions existing in the literature are also obtained as the limiting cases of our solutions.


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