Application of Daftardar Jafari method to first grade MHD squeezing fluid flow in a porous medium with slip boundary condition. (English) Zbl 1470.76115

Summary: In the present work, in the presence of magnetic field and with slip boundary condition, squeezing flow of a Newtonian fluid in a porous medium between two large parallel plates is investigated. The governing equations are transformed to a single nonlinear boundary value problem. Daftardar Jafari Method (DJM) is used to solve the problem in order to obtain the velocity profile of the fluid. By using residual of the problem, the validity of solution is established. The velocity profile is argued through graphs for various values of parameters.


76W05 Magnetohydrodynamics and electrohydrodynamics
76S05 Flows in porous media; filtration; seepage
Full Text: DOI


[1] Papanastasiou, T. C.; Georgiou, G. C.; Alexandrou, A. N., Viscous Fluid Flow (1994), New York, NY, USA: CRC Press, New York, NY, USA
[2] Stefan, M. J., Versuch Uber die scheinbare adhesion, Akademie der Wissenschaften, 69 (1874)
[3] Ran, X. J.; Zhu, Q. Y.; Li, Y., An explicit series solution of the squeezing ow between two innite parallel plates, Communications in Nonlinear Science and Numerical Simulation, 8, 2, 179-184 (2007)
[4] Grimm, R. J., Squeezing flows of Newtonian liquid films an analysis including fluid inertia, Applied Scientific Research, 32, 2, 149-166 (1976) · doi:10.1007/BF00383711
[5] Hughes, W. F.; Elco, R. A., Magnetohydrodynamic lubrication flow between parallel rotating disks, Journal of Fluid Mechanics, 13, 21-32 (1962) · doi:10.1017/S0022112062000464
[6] Kamiyama, S., Inertia effects in MHD hydrostatic thrust bearing, Journal of Tribology, 91, 4, 589-596 (1969) · doi:10.1115/1.3555005
[7] Hamza, E. A., The magnetohydrodynamic squeeze film, Journal of Tribology, 110, 2, 375-377 (1988)
[8] Bhattacharyya, S.; Pal, A., Unsteady MHD squeezing flow between two parallel rotating discs, Mechanics Research Communications, 24, 6, 615-623 (1997) · Zbl 0914.76091
[9] Navier, C. L. M. H., Sur les lois de l’équilibre et dumouvement des corps solides elastiques, Bulletin des Sciences par la Societe Philomatique de Paris, 177-181 (1823)
[10] Roux, C. L., Existence and uniqueness of the flow of second-grade fluids with slip boundary conditions, Archive for Rational Mechanics and Analysis, 148, 4, 309-356 (1999) · Zbl 0934.76005 · doi:10.1007/s002050050164
[11] Rhooades, L. J.; Resnic, R.; O’Bradovich, T.; Stegman, S., Abrasiveflow machining of cylinder heads and its positive effects on performance and cost characteristics (1996), Dearborn, Mich, USA: SAE International, Dearborn, Mich, USA
[12] Ullah, I.; Khan, H.; Rahim, M. T., Approximation of first grade MHD squeezing fluid flow with slip boundary condition using DTM and OHAM, Mathematical Problems in Engineering, 2013 (2013) · Zbl 1299.76315 · doi:10.1155/2013/816262
[13] Hayat, T.; Abelman, S., A numerical study of the influence of slip boundary condition on rotating flow, International Journal of Computational Fluid Dynamics, 21, 1, 21-27 (2007) · Zbl 1184.76901 · doi:10.1080/10618560701347003
[14] Abelman, S.; Momoniat, E.; Hayat, T., Steady MHD flow of a third grade fluid in a rotating frame and porous space, Nonlinear Analysis: Real World Applications, 10, 6, 3322-3328 (2009) · Zbl 1269.76004 · doi:10.1016/j.nonrwa.2008.10.067
[15] Ebaid, A., Effects of magnetic field and wall slip conditions on the peristaltic transport of a Newtonian fluid in an asymmetric channel, Physics Letters A: General, Atomic and Solid State Physics, 372, 24, 4493-4499 (2008) · Zbl 1221.76043 · doi:10.1016/j.physleta.2008.04.031
[16] Daftardar-Gejji, V.; Jafari, H., An iterative method for solving nonlinear functional equations, Journal of Mathematical Analysis and Applications, 316, 2, 753-763 (2006) · Zbl 1087.65055 · doi:10.1016/j.jmaa.2005.05.009
[17] Bhalekar, S.; Daftardar-Gejji, V., New iterative method: application to partial differential equations, Applied Mathematics and Computation, 203, 2, 778-783 (2008) · Zbl 1154.65363 · doi:10.1016/j.amc.2008.05.071
[18] Ullah, I.; Khan, H.; Rahim, M. T., Numerical solutions of higher order nonlinear boundary value problems by new iterative method, Applied Mathematical Sciences, 7, 49-52, 2429-2439 (2013)
[19] Daftardar-Gejji, V.; Bhalekar, S., Solving fractional boundary value problems with Dirichlet boundary conditions using a new iterative method, Computers & Mathematics with Applications, 59, 5, 1801-1809 (2010) · Zbl 1189.35357 · doi:10.1016/j.camwa.2009.08.018
[20] Khan, H.; Islam, S.; Ali, J.; Ali Shah, I., Comparison of different analytic solutions to axisymmetric squeezing fluid flow between two infinite parallel plates with slip boundary conditions, Abstract and Applied Analysis, 2012 (2012) · Zbl 1235.76028 · doi:10.1155/2012/835268
[21] ullah, I.; Khan, H.; Rahim, M. T., Numerical solutions of fifth and sixth order nonlinear boundary value problems by Daftardar Jafari method, Journal of Computational Engineering, 2014 (2014) · doi:10.1155/2014/286039
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