Peristaltic Transport of MHD Walters B Fluid Through Porous Medium with Heat Transfer

K. Ramesh1, M. Devakar2
1Department of Mathematics, Lovely Professional University, Jalandhar, India
2Department of Mathematics, Visvesvaraya National Institute of Technology, Nagpur, India

Tóm tắt

This paper is devoted to the study of the peristaltic flow of a magnetohydrodynamic Walters B fluid through porous medium in a vertical asymmetric channel with heat transfer. The flow is investigated in the wave frame of reference moving with constant velocity with the wave. The non-linear governing partial differential equations are solved using perturbation technique by taking wave number as a small parameter. The expressions for pressure difference and frictional forces are calculated using numerical integration. The graphs are plotted to discuss the variation of velocity, pressure gradient, temperature, heat transfer coefficient, pressure difference, frictional force and trapping for the different flow parameters. It is observed from our analysis that the trapping bolus and pumping rate increase with increase of heat generation parameter. In all situations, the behavior of Hartmann number and Darcy number is always opposite.

Tài liệu tham khảo

Abd-Alla AM, Abo-Dahab SM, Albalawi MM (2014) Magnetic field and gravity effects on peristaltic transport of a Jeffrey fluid in an asymmetric channel. Abstr Appl Anal 2014(2014):896121. doi:10.1155/2014/896121 Abd-Elmaboud Y, Mekheimer KhS, Abdellateef AI (2013) Thermal properties of Couple-stress fluid flow in an asymmetric channel with peristalsis. J Heat Transf 135(4):044502 Abo-Eldahab E, Barakat E, Nowar Kh (2012) Hall currents and heat transfer effects on peristaltic transport in a vertical asymmetric channel through a porous medium. Math Probl Eng 2012(2012):840203. doi:10.1155/2012/840203 Akbar NS, Nadeem S (2014) Convective heat transfer of a Sutterby fluid in an inclined asymmetric channel with partial slip. Heat Transf Res 45(3):219–240 Akbar NS, Hayat T, Nadeem S, Hendi Awatif A (2011) Effects of slip and heat transfer on the peristaltic flow of a third order fluid in an inclined asymmetric channel. Int J Heat Mass Transf 54:1654–1664 Akbar NS, Raza M, Ellahi R (2015) Influence of induced magnetic field and heat flux with the suspension of carbon nanotubes for the peristaltic flow in a permeable channel. J Magn Magn Mater 381:405–415 Ali N, Hayat T (2008) Peristaltic flow of a micropolar fluid in an asymmetric channel. Comput Math Appl 55:589–608 Ellahi R (2013) The effects of MHD and temperature dependent viscosity on the flow of non-Newtonian nanofluid in a pipe: analytical solutions. Appl Math Model 37(3):1451–1467 Ellahi R, Aziz S, Zeeshan A (2013) Non-Newtonian nanofluid flow through a porous medium between two coaxial cylinders with heat transfer and variable viscosity. J Porous Media 16(3):205–216 Ellahi R, Bhatti MM, Riaz A, Sheikholeslami M (2014) Effects of magnetohydrodynamics on peristaltic flow of Jeffrey fluid in a rectangular duct through a porous medium. J Porous Media 17(2):143–157 Elshehawey EF, Eldabe NT, Elghazy EM, Ebaid A (2006) Peristaltic transport in an asymmetric channel through a porous medium. Appl Math Comput 182(1):140–150 Haroun MH (2007) Effect of Deborah number and phase difference on peristaltic transport of a third-order fluid in an asymmetric channel. Commun Nonlinear Sci Numer Simul 12:1464–1480 Hayat T, Ali N, Asghar S (2007) Peristaltic motion of a Burger’s fluid in a planar channel. Appl Math Comput 186(1):309–319 Hayat T, Alvi Nida, Ali N (2008) Peristaltic mechanism of a Maxwell fluid in an asymmetric channel. Nonlinear Anal Real World Appl 9:1474–1490 Hayat T, Umar Qureshi M, Hussain Q (2009) Effect of heat transfer on the peristaltic flow of an electrically conducting fluid in a porous space. Appl Math Model 33:1862–1873 Hayat T, Noreen S, Ali N, Abbasbanday S (2012) Peristaltic motion of Phan-Thien-Tanner fluid in a planar channel. Numer Methods Partial Differ Equ 28(3):737–748 Hina S, Hayat T, Asghar S, Obaidat S (2012) Peristaltic flow of Maxwell fluid in an asymmetric channel with wall properties. Int J Phys Sci 7(14):2145–2155 Khan AA, Ellahi R, Vafai K (2012) Peristaltic transport of a Jeffrey fluid with variable viscosity through a porous Medium in an asymmetric channel. Adv Math Phys 2012(2012):169642. doi:10.1155/2012/169642 Mehmood OU, Shafie S, Mustapha N (2011) Peristaltic transport of Walters B fluid in an asymmetric channel. Int J Appl Math Mech 7(21):1–19 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 Mekheimer KhS, Husseny SZA, Abd-Elmaboud Y (2009) Effects of heat transfer and space porosity on peristaltic flow in a vertical asymmetric channel. Numer Methods Partial Differ Equ 26(4):747–770 Mernone AV, Mazumdar JN (2002) A mathematical study of peristaltic transport of a Casson fluid. Math Comput Model 35:895–912 Mishra M, Rao AR (2003) Peristaltic transport of a Newtonian fluid in an asymmetric channel. Z Angew Math Phys 54:532–550 Misra JC, Maiti S, Shit GC (2008) Peristaltic transport of a physiological fluid in an asymmetric porous channel in the presence of an external magnetic field. J Mech Med Biol 8(4):507–525 Nadeem S, Akbar NS (2010) Influence of heat transfer on peristaltic transport of a Johnson–Segalman fluid in an inclined asymmetric channel. Commun Nonlinear Sci Numer Simul 15:2860–2877 Nadeem S, Akram S (2009) Peristaltic transport of a hyperbolic tangent fluid model in an asymmetric channel. Z Naturforsch 64(a):559–567 Nadeem S, Akram S (2010a) Peristaltic flow of a Williamson fluid in an asymmetric channel. 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, Akram S (2010c) Heat transfer in a peristaltic flow of MHD fluid with partial slip. Commun Nonlinear Sci Numer Simul 15:312–321 Nadeem S, Akram S (2011) Peristaltic flow of a couple stress fluid under the effect of induced magnetic field in an asymmetric channel. Arch Appl Mech 81:97–109 Naga Rani P, Sarojamma G (2004) Peristaltic transport of a Casson fluid in an asymmetric channel. Australas Phys Eng Sci Med 27(2):49–59 Noreen S, Alsaedi A, Hayat T (2012) Peristaltic flow of pseudoplastic fluid in an asymmetric channel. J Appl Mech 79(5):054501 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 Ramesh K, Devakar M (2015a) The influence of heat transfer on peristaltic transport of MHD second grade fluid through porous medium in a vertical asymmetric channel. J Appl Fluid Mech 8(3):351–365 Ramesh K, Devakar M (2015b) Magnetohydrodynamic peristaltic transport of couple stress fluid through porous medium in an inclined asymmetric channel with heat transfer. J Magn Magn Mater 394:335–348 Ramesh K, Devakar M (2016) Effect of heat transfer on the peristaltic flow of Walters B fluid in a vertical channel with an external magnetic field. J Aerosp Eng 29(2):1–15 Reddy SMV, Rao AR, Sreenadh S (2007) Peristaltic motion of a power-law fluid in an asymmetric channel. Int J Non-Linear Mech 42:1153–1161 Sheikholeslami M, Ellahi R, Ashorynejad HR, Domairry G, Hayat T (2014) Effects of heat transfer in flow of nanofluids over a permeable stretching wall in a porous medium. J Comput Theoret Nanosci 11(2):486–496 Tripathi D (2011) Peristaltic transport of a viscoelastic fluid in a channel. Acta Astronaut 68:1379–1385 Tripathi D, Pandey SK, Das S (2010) Peristaltic flow of viscoelastic fluid with fractional Maxwell model through a channel. Appl Math Comput 215:3645–3654 Wang Y, Ali N, Hayat T (2009) Peristaltic motion of a magnetohydrodynamic generalized second-order fluid in an asymmetric channel. Numer Methods Partial Differ Equ 27:415–435 Yildirim A, Sezer SA (2010) Effects of partial slip on the peristaltic flow of a MHD Newtonian fluid in an asymmetric channel. Math Comput Model 52:618–625 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