Effects of partial slip on the peristaltic flow of a MHD Newtonian fluid in an asymmetric channel. (English) Zbl 1201.76318

Yıldırım, Ahmet; Sezer, Sefa Anıl

Math. Comput. Modelling 52, No. 3-4, 618-625 (2010).

Summary: The effects of partial slip on the peristaltic flow of a MHD Newtonian fluid in an asymmetric channel are studied analytically and numerically. The governing equations of motion and energy are simplified using a long wavelength approximation. A closed form solution of the momentum equation is obtained by the homotopy perturbation method (HPM) and an exact solution of the energy equation is presented in the presence of the viscous dissipation term. The expression for pressure rise is calculated using numerical integration. Also, we discussed the trapping phenomena. The graphical results are presented to interpret various physical parameter of interest.

MSC:

76W05	Magnetohydrodynamics and electrohydrodynamics
65M99	Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
76Z05	Physiological flows

Keywords:

homotopy perturbation method; heat transfer; Newtonian fluid; partial slip

References:

[1]	He, J. H., Application of homotopy perturbation method to nonlinear wave equations, Chaos, Solitons and Fractals, 26, 695-700 (2005) · Zbl 1072.35502
[2]	He, J. H., Homotopy perturbation method for bifurcation of nonlinear problems, International Journal of Nonlinear Sciences and Numerical Simulation, 6, 207 (2005) · Zbl 1401.65085
[3]	He, J. H., Homotopy perturbation method for solving boundary value problems, Physics Letters A, 350, 87 (2006) · Zbl 1195.65207
[4]	He, J. H., Homotopy perturbation technique, Computational Methods in Applied Mechanics and Engineering, 178, 257 (1999) · Zbl 0956.70017
[5]	He, J. H., Recent development of the homotopy perturbation method, Topological Methods in Nonlinear Analysis, 31, 205 (2008) · Zbl 1159.34333
[6]	He, J. H., Some asymptotic methods for strongly nonlinear equations, International Journal of Modern Physics B, 20, 1141 (2006) · Zbl 1102.34039
[7]	He, J. H., New interpretation of homotopy perturbation method, International Journal of Modern Physics B, 20, 2561 (2006)
[8]	He, J. H., An elementary introduction to recently developed asymptotic methods and nanomechanics in textile engineering, International Journal of Modern Physics B, 22, 3487 (2008) · Zbl 1149.76607
[9]	Yıldırım, A.; Öziş, T., Solutions of singular IVPs of Lane-Emden type by homotopy perturbation method, Physics Letters A, 369, 70 (2007) · Zbl 1209.65120
[10]	Yıldırım, A., Solution of BVPs for fourth-order integro-differential equations by using homotopy perturbation method, Computers & Mathematics with Applications, 56, 3175-3180 (2008) · Zbl 1165.65377
[11]	Yıldırım, A., The homotopy perturbation method for approximate solution of the modified KdV equation, Zeitschrift für Naturforschung A, A Journal of Physical Sciences, 63a, 621 (2008)
[13]	Mohyud-Din, S. T.; Noor, M. A.; Noor, K. I., Travelling wave solutions of seventh-order generalized KdV equations using He’s polynomials, International Journal of Nonlinear Sciences and Numerical Simulation, 10, 2, 223-229 (2009)
[14]	Shakeri, F.; Dehghan, M., Inverse problem of diffusion equation by He’s homotopy perturbation method, Physica Scripta, 75, 551 (2007) · Zbl 1110.35354
[15]	Dehghan, M.; Shakeri, F., Solution of a partial differential equation subject to temperature Overspecification by He’s homotopy perturbation method, Physica Scripta, 75, 778 (2007) · Zbl 1117.35326
[16]	Shakeri, F.; Dehghan, M., Solution of the delay differential equations via homotopy perturbation method, Mathematical and Computer Modelling, 48, 486 (2008) · Zbl 1145.34353
[18]	Ganji, D. D.; Rajabi, A., Assessment of homotopy-perturbation and perturbation methods in heat radiation equations, International Communications in Heat Mass Transfer, 33, 391-400 (2006)
[19]	Ganji, D. D.; Sadighi, A., Application of He’s homotopy-perturbation method to nonlinear coupled systems of reaction-diffusion equations, International Journal of Nonlinear Sciences and Numerical Simulation, 7, 2, 411-418 (2006)
[20]	Donald Ariel, P., Homotopy perturbation method and the natural convection flow of a third grade fluid through a circular tube, Nonlinear Science Letters A, 1, 43-52 (2010)
[21]	Golbabai, A.; Sayevand, K., The homotopy perturbation method for multi-order time fractional differential equations, Nonlinear Science Letters A, 1, 147-154 (2010)
[22]	Elshehawey, E. F.; Eladabe, N. T.; Elghazy, E. M.; Ebaid, A., Peristaltic transport in an asymmetric channel through a porous medium, Applied Mathematics and Computation, 182, 140-150 (2006) · Zbl 1149.76670
[23]	Hayat, T.; Hussain, Q.; Ali, N., Influence of partial slip on the peristaltic flow in a porous medium, Physica A, 387, 3399-3409 (2008) · Zbl 1159.74303
[24]	Hayat, T.; Ali, N.; Asghar, S.; Siddiqui, A. M., Exact peristaltic flow in tubes with an endoscope, Applied Mathematics and Computation, 182, 359-368 (2006) · Zbl 1103.76073
[25]	Abd El-Naby, A. H.; El-Misiery, A. E.M., Effects of an endoscope and generalized Newtonian fluid on peristaltic motion, Applied Mathematics and Computation, 128, 19-35 (2002) · Zbl 1126.76403
[26]	Hayat, T.; Ahmad, N.; Ali, N., Effects of an endoscope and magnetic field on the peristalsis involving Jeffrey fluid, Communications in Nonlinear Sciences and Numerical Simulation, 13, 1581-1591 (2008) · Zbl 1221.76078
[27]	Radhakrishnamacharya, G.; Srinivasulu, Ch., Influence of wall properties on peristaltic transport with heat transfer, Comptes Rendus Mechanics, 335, 369-373 (2007) · Zbl 1144.76067
[28]	Radhakrishnamacharya, G.; Radhakrishna Murthy, V., Heat transfer to peristaltic transport in a non-uniform channel, Defence Science Journal, 43, 275-280 (1993)
[29]	Nadeem, S.; Akram, Safia, Heat transfer in a peristaltic flow of MHD fluid with partial slip, Communications in Nonlinear Sciences and Numerical Simulation, 15, 312-321 (2010) · Zbl 1221.76232