Abstract
This investigation deals with the influence of heat and mass transfer on magnetohydrodynamic peristaltic flow of Pseudoplastic fluid in a vertical asymmetric channel through porous medium. The flow is examined in the wave frame of reference moving with the velocity of the wave. For formulation of the problem, long wavelength and low Reynolds number assumptions are taken into account. The perturbation solution has been derived for the stream function and pressure gradient. The pressure difference is calculated numerically. The influence of various parameters of interest on velocity, pressure gradient, temperature, concentration, pressure difference, heat transfer coefficient and trapping has been investigated graphically. The graphical results are also discussed for four different wave shapes. It is found that, in all the cases the magnetic parameter and Darcy number have opposite effect on the flow variables. The size of the trapped bolus increases from porous medium to non-porous medium and it decreases with increase of magnetic effects.
Similar content being viewed by others
References
Abd Elmaboud Y, Mekheimer KhS (2011) Non-linear peristaltic transport of a second order fluid through a porous medium. Appl Math Model 35:2695–2710
Abd-Alla AM, Abo-Dahab SM, El-Shahrany HD (2013) Effects of rotation and magnetic field on the nonlinear peristaltic flow of a second-order fluid in an asymmetric channel through a porous medium. Chin Phys B 22(7):074702
Akbar NS, Nadeem S (2012) Thermal and velocity slip effects on the peristaltic flow of a six constant Jeffrey’s fluid model. Int J Heat Mass Transf 55:3964–3970
Akbar NS, Raza M, Ellahi R (2014) Influence of heat generation and heat flux on peristaltic flow with interacting nanoparticles. Eur Phys J Plus 129:185
Deepa G, Murali G (2014) Effects of viscous dissipation on unsteady MHD free convective flow with thermophoresis past a radiate inclined permeable plate. Iran J Sci Technol 38(A3):379–388
Ellahi R, Hameed M (2012) Numerical analysis of steady non-Newtonian flows with heat transfer analysis, MHD and nonlinear slip effects. Int J Numer Meth Heat Fluid Flow 22(1):24–38
Ellahi R, Shivanian E, Abbasbandy S, Rahman SU, Hayat T (2012) Analysis of steady flows in viscous fluid with heat/mass transfer and slip effects. Int J Heat Mass Transf 55:6384–6390
Ellahi R, Riaz A, Nadeem S, Mushtaq M (2013) Series solutions of magnetohydrodynamic peristaltic flow of a Jeffrey fluid in eccentric cylinders. Appl Math Inf Sci 7(4):1441–1449
Ellahi R, Bhatti MM, Vafai K (2014) Effects of heat and mass transfer on peristaltic flow in a non-uniform rectangular duct. Int J Heat Mass Transf 71:706–719
Hayat T, Noreen S (2010) Peristaltic transport of fourth grade fluid with heat transfer and induced magnetic field. CR Mec 338:518–528
Hayat T, Afsar A, Khan M, Asghar S (2007) Peristaltic transport of a third order fluid under the effect of a magnetic field. Comput Math Appl 53:1074–1087
Hayat T, Noreen S, Alhothuali MS, Asghar S, Alhomaidan A (2012) Peristaltic flow under the effects of an induced magnetic field and heat and mass transfer. Int J Heat Mass Transf 55:443–452
Hayat T, Abbasi FM, Al-Yami Maryem, Monaquel Shatha (2014a) Slip and Joule heating effects in mixed convection peristaltic transport of nano fluid with Soret and Dufour effects. J Mol Liq 194:93–99
Hayat T, Yasmin H, Al-Yami M (2014b) Soret and Dufour effects in peristaltic transport of physiological fluids with chemical reaction: a mathematical analysis. Comput Fluids 89:242–253
Hina S, Hayat T, Asghar S, Alhothuali MS, Alhomaidan A (2012) Magnetohydrodynamic non-linear peristaltic flow in a compliant walls channel with heat and mass transfer. J Heat Transf 134:071101
Kandasamy R, Hashim I, Khamis AB, Muhaimin I (2007) Combined heat and mass transfer in MHD free convection from a wedge with Ohmic heating and viscous dissipation in the presence of suction or injection. Iran J Sci Technol Trans A 31(A2):151–162
Khan AA, Ellahi R, Gulzar MM, Sheikholeslami M (2014) Effects of heat transfer on peristaltic motion of Oldroyd fluid in the presence of inclined magnetic field. J Magn Magn Mater 72:97–106
Mehmood OU, Mustapha N, Shafie S (2012) Heat transfer on peristaltic flow of fourth grade fluid in inclined asymmetric channel with partial slip. Appl Math Mech Engl Ed 33(10):1313–1328
Mustafa M, Abbasbandy S, Hina S, Hayat T (2014) Numerical investigation on mixed convective peristaltic flow of fourth grade fluid with Dufour and Soret effects. J Taiwan Inst Chem Eng 45:308–316
Nadeem S, Akram S (2010a) Peristaltic flow of a Williamson fluid in an asymmetric channel. Commun Nonlinear Sci Numer Simul 15:1705–1716
Nadeem S, Akram S (2010b) Influence of inclined magnetic field on peristaltic flow of a Williamson fluid model in an inclined symmetric or asymmetric channel. Math Comput Model 52:107–119
Nadeem S, Riaz A, Ellahi R, Akbar NS (2014) Effects of heat and mass transfer on peristaltic flow of a nanofluid between eccentric cylinders. Appl Nanosci 4:393–404
Pandey SK, Chaube MK (2011) Peristaltic flow of a micropolar fluid through a porous medium in the presence of an external magnetic field. Commun Nonlinear Sci Numer Simul 16:3591–3601
Radhakrishnamacharya G, Srinivasulu Ch (2007) Influence of wall properties on peristaltic transport with heat transfer. CR Mec 335:369–373
Rana GC, Thakur RC (2011) Combined effect of suspended particles and rotation on thermosolutal convection in a viscoelastic fluid saturating a Darcy-Brinkman porous medium. Iran J Sci Technol 37(A1):319–325
Saleem M, Haider A (2014) Heat and mass transfer on the peristaltic transport of non-Newtonian fluid with creeping flow. Int J Heat Mass Transf 68:514–526
Sheikholeslami M, Ellahi R, Ashorynejad HR, Domairry G, Hayat T (2014a) Effects of heat transfer in flow of nanofluids over a permeable stretching wall in a porous medium. J Comput Theor Nanosci 11(2):486–496
Sheikholeslami M, Gorji Bandpy M, Ellahi R (2014b) Effects of MHD on Cu–water nanofluid flow and heat transfer by means of CVFEM. J Magn Magn Mater 349:188–200
Srinivas S, Muthuraj R (2011) Effects of chemical reaction and space porosity on MHD mixed convective flow in a vertical asymmetric channel with peristalsis. Math Comput Model 54:1213–1227
Srinivas S, Pushparaj V (2008) Non-linear peristaltic transport in an inclined asymmetric channel. Commun Nonlinear Sci Numer Simul 13:1782–1795
Tripathi D (2011) Peristaltic transport of a viscoelastic fluid in a channel. Acta Astronaut 68:1379–1385
Tripathi D (2012) Peristaltic hemodynamic flow of couple stress fluids through a porous medium with slip effect. Transp Porous Media 92:559–572
Tripathi D (2013) Study of transient peristaltic heat flow through a finite porous channel. Math Comput Model 57:1270–1283
Vajravelu K, Sreenadh S, Lakshminarayana P (2011) The influence of heat transfer on peristaltic transport of a Jeffrey fluid in a vertical porous stratum. Commun Nonlinear Sci Numer Simul 16:3107–3125
Zeeshan A, Ellahi R (2013) Series solutions for nonlinear partial differential equations with slip boundary conditions for non-Newtonian MHD fluid in porous space. Appl Math Inf Sci 7(1):257–265
Zeeshan A, Ellahi R, Hassan M (2014) Magnetohydrodynamic flow of water/ethylene glycol based nanofluids with natural convection through a porous medium. Eur Phys J Plus 129:261
Acknowledgements
The authors sincerely thank the reviewers for their valuable comments and suggestions which helped us to improve the presentation of the present paper.
Author information
Authors and Affiliations
Corresponding author
Appendix
Appendix
Rights and permissions
About this article
Cite this article
Ramesh, K., Devakar, M. Magnetohydrodynamic Peristaltic Flow of Pseudoplastic Fluid in a Vertical Asymmetric Channel Through Porous Medium with Heat and Mass Transfer. Iran J Sci Technol Trans Sci 41, 257–272 (2017). https://doi.org/10.1007/s40995-017-0193-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40995-017-0193-1