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Journal of Porous Media

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ISSN Print: 1091-028X

ISSN Online: 1934-0508

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Some MHD Flows of a Second Grade Fluid through the Porous Medium

Volume 11, Issue 4, 2008, pp. 389-400
DOI: 10.1615/JPorMedia.v11.i4.50
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I. Khan
Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000, Pakistan
Rahmat Ellahi
Professor, Faculty of Sciences, International Islamic University, Islamabad, Pakistan; Chair Professor Center for Modeling & Computer Simulation, Research Institute, King Fahd University of Petroleum & Minerals, Dhahran-31261, Saudi Arabia; Fulbright Fellow Department of Mechanical Engineering University of California Riverside, Riverside, CA, USA
Constantin Fetecau
Academy of Romanian Scientists, Bucuresti 050094, Romania

ABSTRACT

In this article, we investigate the effects of magnetic field and porous medium on some unidirectional flows of a second grade fluid. These magnetohydrodynamic (MHD) flows are produced by the application of periodic pressure gradient or by the impulsive motion of one or two boundaries or by an oscillating plate. Modified Darcy's law has been used for the flow modeling. Seven illustrative examples have been taken into account and exact analytic solutions for velocity are obtained. Besides that analytic expressions for frictional forces have been established. The corresponding results of velocity and frictional forces in the absence of a porous medium and applied magnetic field Rajagopal, 1982; Hayat et al., 2000, can be obtained from the present analysis by taking M → 0 and K → 0. The similar results for a Newtonian fluid can also be gotten as a limiting case.

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  2. Akram Safia, Nadeem S., Influence of induced magnetic field and heat transfer on the peristaltic motion of a Jeffrey fluid in an asymmetric channel: Closed form solutions, Journal of Magnetism and Magnetic Materials, 328, 2013. Crossref

  3. Jamil Muhammad, Khan Najeeb Alam, Rauf Abdul, Oscillating Flows of Fractionalized Second Grade Fluid, ISRN Mathematical Physics, 2012, 2012. Crossref

  4. Nadeem S., Akram Safia, Influence of inclined magnetic field on peristaltic flow of a Jeffrey fluid with heat and mass transfer in an inclined symmetric or asymmetric channel, Asia-Pacific Journal of Chemical Engineering, 7, 1, 2012. Crossref

  5. Mekheimer Kh.S., Salem A.M., Zaher A.Z., Peristatcally induced MHD slip flow in a porous medium due to a surface acoustic wavy wall, Journal of the Egyptian Mathematical Society, 22, 1, 2014. Crossref

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  10. Awais M., Applications of the Numerical Inversion of the Laplace transform to unsteady problems of the third grade fluid, Applied Mathematics and Computation, 250, 2015. Crossref

  11. Jha Basant K., Aina Babatunde, Isa Sani, MHD natural convection flow in a vertical micro-concentric-annuli in the presence of radial magnetic field: An exact solution, Ain Shams Engineering Journal, 7, 4, 2016. Crossref

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  25. Sarwar Shakila, Nazar Mudassar, Imran M. A., Influence of slip over an exponentially moving vertical plate with Caputo-time fractional derivative, Journal of Thermal Analysis and Calorimetry, 145, 5, 2021. Crossref

  26. Ghalib M. Mansha, Zafar Azhar A., Riaz M. Bilal, Hammouch Z., Shabbir Khurram, Analytical approach for the steady MHD conjugate viscous fluid flow in a porous medium with nonsingular fractional derivative, Physica A: Statistical Mechanics and its Applications, 554, 2020. Crossref

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