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Peristaltic transport of a Newtonian fluid in a vertical asymmetric channel with heat transfer and porous medium. (English) Zbl 1172.76051
Summary: The problem of peristaltic flow of a Newtonian fluid with heat transfer in a vertical asymmetric channel through porous medium is studied under long-wavelength and low-Reynolds number assumptions. The flow is examined in a wave frame of reference moving with the velocity of the wave. The channel asymmetry is produced by choosing the peristaltic wave train on the walls to have different amplitudes and phase. The analytical solution has been obtained for the temperature, from which an axial velocity, stream function and pressure gradient have been derived. The effects of permeability parameter, Grashof number, heat source/sink parameter, phase difference, varying channel width and wave amplitudes on the pressure gradient, velocity, pressure drop, the phenomenon of trapping and shear stress are discussed numerically and explained graphically.

MSC:
76S05 Flows in porous media; filtration; seepage
76D05 Navier-Stokes equations for incompressible viscous fluids
80A20 Heat and mass transfer, heat flow (MSC2010)
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[1] Eytan, O.; Elad, D., Analysis of intra-uterine fluid motion induced by uterine contractions, Bull. math. biol., 61, 221-238, (1999) · Zbl 1323.92063
[2] El Shehawey, E.F.; Husseny, S.Z.A., Effects of porous boundaries on peristaltic transport through a porous medium, Acta mech., 143, 165-177, (2000) · Zbl 0969.76084
[3] EL Shehawey, E.F.; EL Sebaei, W., Peristaltic transport in a cylindrical tube through a porous medium, Internat. J. math. math. sci., 24, 217-230, (2000) · Zbl 0962.76101
[4] Mishra, Manoranjan; Ramachandra Rao, Adabala, Peristaltic transport of a Newtonian fluid in an asymmetric channel, Zamp, 54, 532-550, (2003) · Zbl 1099.76545
[5] Hayat, T.; Ali, N.; Asghar, S., Hall effects on peristaltic flow of a Maxwell fluid in a porous medium, Phys. lett. A, 363, 397-403, (2007) · Zbl 1197.76126
[6] Srinivas, S.; Pushparaj, V., Non-linear peristaltic transport in an inclined asymmetric channel, Commun. nonlinear sci. numer. simul., 13, 1782-1795, (2008)
[7] Ali, Nasir; Hayat, Tasawar; Asghar, Saleem, Peristaltic flow of a Maxwell fluid in a channel with compliant walls, Chaos, solitons & fractals, 39, 407-416, (2009) · Zbl 1197.76017
[8] Kothandapani, M.; Srinivas, S., Non-linear peristaltic transport of Newtonian fluid in an inclined asymmetric channel through a porous medium, Phys. lett. A, 372, 1265-1276, (2008) · Zbl 1217.76105
[9] Hariharan, Prasanna; Seshadri, V.; Banerjee, Rupak K., Peristaltic transport of non-Newtonian fluid in a diverging tube with different waveforms, Math. comput. model., 48, 998-1017, (2008) · Zbl 1187.76606
[10] Asif Ikbal, Md.; Chakravarty, Santabrata; Mandal, Prashanta Kumar, An unsteady transport phenomenon of non-Newtonian fluid – a generalized approach, Appl. math. comput., 201, 16-34, (2008) · Zbl 1228.76205
[11] Vajravelu, K.; Radhakrishnamacharya, G.; Radhakrishnamurty, V., Peristaltic flow and heat transfer in a vertical porous annulus, with long-wavelength approximation, Int. J. nonlinear mech., 42, 754-759, (2007) · Zbl 1200.76192
[12] Radhakrishnamacharya, G.; Srinivasulu, Ch., Influence of wall properties on peristaltic transport with heat transfer, C.R. mec., 335, 369-373, (2007) · Zbl 1144.76067
[13] Srinivas, S.; Kothandapani, M., Peristaltic transport in an asymmetric channel with heat transfer – a note, Int. comm., heat and mass transfer, 35, 514-522, (2008) · Zbl 1217.76105
[14] Mekheimer, Kh.S.; Abd elmaboud, Y., The influence of heat transfer and magnetic field on peristaltic transport of a Newtonian fluid in a vertical annulus: application of an endoscope, Phys. lett. A, 372, 1657-1665, (2008) · Zbl 1217.76106
[15] Ali, N.; Hayat, T.; Sajid, M., Peristaltic flow of a couple stress fluid in asymmetric channel, Biorheology, 44, 125-138, (2007)
[16] Subba Reddy, M.V.; Ramachandra Rao, A.; Sreenath, S., Peristaltic motion of a power-law fluid in an asymmetric channel, Int. J. non-linear mech., 42, 1153-1161, (2007)
[17] Kothandapani, M.; Srinivas, S., On the influence of wall properties in the MHD peristaltic transport with heat transfer and porous medium, Phys. lett. A, 372, 4586-4591, (2008) · Zbl 1221.76044
[18] Hayat, T.; Javed, Merylam; Asghar, S., MHD peristaltic motion of Johnson-Segalman fluid in a channel with compliant walls, Phys. lett. A, 372, 5026-5036, (2008) · Zbl 1221.76219
[19] Kothandapani, M.; Srinivas, S., Peristaltic transport of a Jeffery fluid under the effect of magnetic field in an asymmetric channel, Int. J. non-linear mech., 43, 915-924, (2008)
[20] Srinivas, S.; Kothandapani, M., The influence of heat and mass transfer on MHD peristaltic flow through a porous space with complaint walls, Appl. math. comput., 213, 197-208, (2009) · Zbl 1165.76052
[21] Nield, D.A.; Bejan, A., Convection in porous media, (1999), Springer New York · Zbl 0924.76001
[22] ()
[23] Pop, I.; Ingham, D.B., Convective heat transfer: computational and mathematical of modeling viscous fluids and porous media, (2001), Pergamon Oxford
[24] Bejan, A.; Kraus, A.D., Heat transfer handbook, (2003), Wiley New York
[25] Canny, M.J.; Phillips, O.M., Quantitative aspects of a theory of translocation, Ann. botany, 27, 379-402, (1963)
[26] Aikman, D.P.; Anderson, W.P., A quantitative investigation of a peristaltic model for phloem translocation, Ann. botany, 35, 761-772, (1971)
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