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Peristaltic transport in an asymmetric channel through a porous medium. (English) Zbl 1149.76670
Summary: The problem of peristaltic transport of an incompressible viscous fluid in an asymmetric channel through a porous medium is analyzed. The flow is investigated in a wave frame of reference moving with velocity of the wave under the assumptions of long-wavelength and low-Reynolds number. An explicit form of the stream function is obtained by using Adomian decomposition method. The analysis showed that transport phenomena are strongly dependent on the phase shift between the two walls of the channel. It is indicated that the axial velocity component U in fixed frame increases with increasing the permeability parameter. In the case of high permeability parameter (as $K \rightarrow \infty )$, our results are in agreement with {\it M. Mishra} and {\it A. Ramachandra Rao} [Z. Angew. Math. Phys. 54, No. 3, 532--550 (2003; Zbl 1099.76545)] and {\it O. Eytan, D. Elad} [Analysis of intra-uterine fluid motion induced by uterine contractions, Bull. Math. Biol. 61, 221 (1999)]. The results given in this paper may throw some light on the fluid dynamic aspects of the intra-uterine fluid flow through a porous medium.

MSC:
76S05Flows in porous media; filtration; seepage
74F10Fluid-solid interactions
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Full Text: DOI
References:
[1] Adomian, G.: Solving frontier problems of physics: the decomposition method. (1994) · Zbl 0802.65122
[2] Barton, C.; Raynor, S.: Peristaltic flow in tubes. Bull. math. Biophys. 30, 663 (1968) · Zbl 0167.48605
[3] Burns, J. C.; Parkes, T.: Peristaltic motion. J. fluid mech. 29, 731 (1967)
[4] De Vries, K.; Lyons, E. A.; Ballard, J.; Levi, C. S.; Lindsay, D. J.: Contractions of the inner third of myometrium. Am. J. Obstetrics gynecol. 162, 679 (1990)
[5] El Sayed, M. F.: Electrohydrodynamic instability of two superposed viscous streaming fluids through porous medium. Can. J. Phys. 75, 499 (1997)
[6] Eytan, O.; Elad, D.: Analysis of intra-uterine fluid motion induced by uterine contractions. Bull. math. Biol. 61, 221 (1999) · Zbl 1323.92063
[7] Eytan, O.; Jaffa, A. J.; Har-Toov, J.; Dalach, E.; Elad, D.: Dynamics of the intrauterine fluid-wall interface. Ann. biomed. Eng. 27, 372 (1999)
[8] Jaffrin, M. Y.: Inertia and streamline curvature on peristaltic pumping. Int. J. Eng. sci. 11, 681 (1973)
[9] T.W. Latham, Fluid Motion in a Peristaltic Pump, M.Sc. Thesis, Massachusetts Institute of Technology, Cambridge, 1966.
[10] Mishra, M.; Rao, A. Ramachandra: Peristaltic transport of a Newtonian fluid in an asymmetric channel. Zamp 53, 532 (2003) · Zbl 1099.76545
[11] Nield, D. A.; Bejan, A.: Convection in porous media. (1992) · Zbl 1256.76004
[12] Raptis, A.; Kafousias, N.; Massalas, C. Z.: Free convection flow through a porous medium bounded by a vertical surface. Z. angew. Math. mech. (ZAMM) 62, 489 (1982) · Zbl 0486.76104
[13] Raptis, A.; Peridikis, C.; Tzivanidis, G.: Free convection flow through a porous medium bounded by a vertical surface. J. phys. D. appl. Phys. 14, 199 (1981)
[14] Rathy, R. K.: An introduction to fluid dynamics. (1976)
[15] Scheidegger, A. E.: The physics of flow through porous media. (1963) · Zbl 0119.45901
[16] A.H. Shapiro, Pumping and retrograde diffusion in peristaltic waves, in: Proceedings of the Workshop in Ureteral Reflux in Children, 1967, p. 109.
[17] Shapiro, A. H.; Jaffrin, M. Y.; Weinberg, S. L.: Peristaltic pumping with long wave lengths at low Reynolds number. J. fluid mech. 37, 799 (1969)
[18] Varshney, C. L.: Fluctuating flow of viscous fluid through a porous medium bounded by a porous plate. Indian J. Pure. appl. Math. 10, 1558 (1979) · Zbl 0416.76049
[19] Yamamoto, K.; Iwamura, N.: Flow with convective acceleration through a porous medium. J. eng. Math. 10, 41 (1976) · Zbl 0376.76066