Abstract
Here an attempt has been made to investigate the magnetohydrodynamic (MHD) flow of a non-Newtonian fluid filling the porous space in a channel with compliant walls. Constitutive equations of a Jeffery fluid are used in the mathematical modeling. The flow is created due to sinusoidal traveling waves on the channel walls. The resulting problem is solved analytically and series solution for a stream function is derived. The effects of pertinent flow parameters are discussed through graphs.
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Abd Elnaby, M.A., Haroun, M.H.: A new model for study the effect of wall properties on peristaltic transport of a viscous fluid. Comm. Nonlinear Sci. Numer. Simul. 13, 752–762 (2008)
Davies, C., Carpenter, P.W.: Instabilities in a plane channel flow between compliant walls. J. Fluid Mech. 352, 205–243 (1997)
Elshahed, M., Haroun, M.H.: Peristaltic transport of Johnson-Segalman fluid under effect of a magnetic field. Math. Problems Eng. 6, 663–667 (2005)
Elshehawey, E.F., Mekheimer, Kh.S.: Couple-stresses in peristaltic transport of fluids. J. Phys. D: Appl. Phys. 27, 1163–1170 (1994)
Fung, Y.C., Yih, C.S.: Peristaltic transport. Trans. ASME J. Appl. Mech. 33, 669–675 (1968)
Haroun, M.H.: Effect of Deborah number and phase difference on peristaltic transport of a third-order fluid in an asymmetric channel. Comm. Nonlinear Sci. Numer. Simul. 12, 1464–1480 (2007)
Hayat, T., Wang, Y., Siddiqui, A.M., Hutter, K., Asghar, S.: Peristaltic transport of a third-order fluid in a circular cylindrical tube. Math. Models Meth. Appl. Sci. 12, 1691–1706 (2002)
Hayat, T., Wang, Y., Siddiqui, A.M., Hutter, K.: Peristaltic motion of Johnson-Segalman fluid in a planar channel. Math. Problems Eng. 1, 1–23 (2003)
Hayat, T., Wang, Y., Hutter, K., Asghar, S., Siddiqui, A.M.: Peristaltic transport of an Oldroyd-B fluid in a planar channel. Math. Problems Eng. 4, 347–376 (2004)
Hayat, T., Mahomed, F.M., Asghar, S.: Peristaltic flow of a magnetohydrodynamic Johnson-Segalman fluid. Nonlinear Dyn. 40, 375–385 (2005)
Hayat, T., Khan, M., Asghar, S., Siddiqui, A.M.: A mathematical model of peristalsis in tubes through a porous medium. J. Porous Media 9, 55–67 (2006)
Hayat, T., Momoniat, E., Mahomed, F.M.: Effect of an endoscope and an electrically conducting third grade fluid on peristaltic motion. Int. J. Modern Phys. B (in press)
Latham, T.W.: Fluid motion in a peristaltic pump. MS Thesis, Massachusetts Institute of Technology, Cambridge AMA (1996)
Mekheimer, Kh.S.: Peristaltic transport of a couple-stress fluid in a uniform and non-uniform channels. Biorheology 39, 755–765 (2002)
Mekheimer, Kh.S.: Peristaltic flow of blood under effect of a magnetic field in non-uniform channels. Appl. Math. Comput. 153, 763–777 (2004)
Mishra, M., Rao, A.R.: Peristaltic transport of a Newtonian fluid in an asymmetric channel. Z. Angew. Math. Phys. 54, 532–540 (2004)
Siddiqui, A.M., Provost, A., Schwarz, W.H.: Peristaltic pumping of a second order fluid in a planar channel. Rheol. Acta 30, 249–262 (1991)
Tan, W.C., Masuoka, T.: Stokes’ first problem for an Oldroyd-B fluid in a porous half space. Phys. Fluid 17, 023101–023107 (2005)
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Hayat, T., Javed, M. & Ali, N. MHD Peristaltic Transport of a Jeffery Fluid in a Channel With Compliant Walls and Porous Space. Transp Porous Med 74, 259–274 (2008). https://doi.org/10.1007/s11242-007-9196-2
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DOI: https://doi.org/10.1007/s11242-007-9196-2