A hydromagnetic flow through porous medium near an accelerating plate in the presence of magnetic field

References

[1] R. Bandelli and K. R. Rajagopal, Start-up flows of second grade fluids in domains with one finite dimension, Internat. J. Nonlinear Mech. 30 (1995), no. 6, 817–839. 10.1016/0020-7462(95)00035-6Search in Google Scholar

[2] C. Fetecau, M. Athar and C. Fetecau, Unsteady flow of a generalized Maxwell fluid with fractional derivative due to a constantly accelerating plate, Comput. Math. Appl. 57 (2009), no. 4, 596–603. 10.1016/j.camwa.2008.09.052Search in Google Scholar

[3] C. Fetecau, C. Fetecau, M. Kamran and D. Vieru, Exact solutions for the flow of a generalized Oldroyd-B fluid induced by a constantly accelerating plate between two side walls perpendicular to the plate, J. Non-Newtonian Fluid Mech. 156 (2009), no. 3, 189–201. 10.1016/j.jnnfm.2008.06.005Search in Google Scholar

[4] S. Hyder and A. M. Shah, Some accelerated flows of generalized Oldroyd-B fluid between two side walls perpendicular to the plate, Nonlinear Anal. Real World Appl. 10 (2009), no. 4, 2146–2150. 10.1016/j.nonrwa.2008.03.023Search in Google Scholar

[5] M. Jamil, A. Rauf, A. A. Zafar and N. A. Khan, New exact analytical solutions for Stokes’ first problem of Maxwell fluid with fractional derivative approach, Comput. Math. Appl. 62 (2011), no. 3, 1013–1023. 10.1016/j.camwa.2011.03.022Search in Google Scholar

[6] J. Kang and M. Xu, An exact solution for flow past an accelerated horizontal plate in a rotating fluid with the generalized Oldroyd-B model, Acta Mech. Sin. 25 (2009), no. 4, 463–469. 10.1007/s10409-009-0243-9Search in Google Scholar

[7] M. Khan, A. Anjum, Q. Haitao and C. Fetecau, On exact solutions for some oscillating motions of a generalized Oldroyd-B fluid, Z. Angew. Math. Phys. 61 (2010), no. 1, 133–145. 10.1007/s00033-009-0004-4Search in Google Scholar

[8] M. Khan, T. Hayat and S. Asghar, Exact solution for MHD flow of a generalized Oldroyd-B fluid with modified Darcy’s law, Internat. J. Engrg. Sci. 44 (2006), no. 5–6, 333–339. 10.1016/j.ijengsci.2005.12.004Search in Google Scholar

[9] Y. Liu, L. Zheng and X. Zhang, Unsteady MHD Couette flow of a generalized Oldroyd-B fluid with fractional derivative, Comput. Math. Appl. 61 (2011), no. 2, 443–450. 10.1016/j.camwa.2010.11.021Search in Google Scholar

[10] A. Mahmood, C. Fetecau, N. A. Khan and M. Jamil, Some exact solutions of the oscillatory motion of a generalized second grade fluid in an annular region of two cylinders, Acta Mech. Sin. 26 (2010), no. 4, 541–550. 10.1007/s10409-010-0353-4Search in Google Scholar

[11] A. M. Mathai, R. K. Saxena and H. J. Haubold, The H-Function: Theory and Applications, Springer, New York, 2010. 10.1007/978-1-4419-0916-9Search in Google Scholar

[12] I. Podlubny, Fractional Differential Equations. An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications, Math. Sci. Eng. 198, Academic Press, San Diego, 1999. Search in Google Scholar

[13] H. T. Qi and M. Y. Xu, Stokes’ first problem for a viscoelastic fluid with the generalized Oldroyd-B model, Acta Mech. Sin. 23 (2007), no. 5, 463–469. 10.1007/s10409-007-0093-2Search in Google Scholar

[14] S. Rivlin and J. L. Ericksen, Stress-deformation relations for isotropic materials, J. Ration. Mech. Anal. 4 (1955), 323–425. 10.1007/978-1-4612-2416-7_61Search in Google Scholar

[15] K. D. Singh and B. P. Garg, Exact solution of an oscillatory free convective MHD flow in a rotating porous channel with radiative heat, Proc. Nat. Acad. Sci. India Sect. A 80 (2010), 81–89. Search in Google Scholar

[16] K. D. Singh and P. Reena, An analysis of an oscillatory rotating MHD Poiseuille flow with injection/suction and Hall currents, Proc. Indian Nat. Sci. Acad. 76 (2010), no. 4, 201–207. Search in Google Scholar

[17] I. N. Sneddon, Fourier Transforms, McGraw-Hill Book, New York, 1951. Search in Google Scholar

[18] W. C. Tan and M. Y. Xu, The impulsive motion of flat plate in a generalized second grade fluid, Mech. Res. Commun. 29 (2002), no. 1, 3–9. 10.1016/S0093-6413(02)00223-9Search in Google Scholar

[19] W. C. Tan and M. Y. Xu, Unsteady flows of a generalized second grade fluid with the fractional derivative model between two parallel plates, Acta Mech. Sin. Engl. Ser. 20 (2004), no. 5, 471–476. 10.1007/BF02484269Search in Google Scholar

[20] D. Tripathi, Peristaltic flow of a fractional second grade fluid through a cylindrical tube, Thermal Sci. 15 (2011), no. 2, S167–S173. 10.2298/TSCI100503061TSearch in Google Scholar

[21] D. Vieru, C. Fetecau and C. Fetecau, Flow of a generalized Oldroyd-B fluid due to a constantly accelerating plate, Appl. Math. Comput. 201 (2008), no. 1–2, 834–842. 10.1016/j.amc.2007.12.045Search in Google Scholar

[22] G. Zaman, S. Islam, Y. H. Kang and I. H. Jung, Blood flow of an Oldroyd-B fluid in a blood vessel incorporating a Brownian stress, Sci. China Phys. Mech. Astron. 55 (2012), no. 2, 125–131. 10.1007/s11433-011-4571-ySearch in Google Scholar