Skip to main content
SpringerLink
Log in

Magnetohydrodynamic Peristaltic Flow of Pseudoplastic Fluid in a Vertical Asymmetric Channel Through Porous Medium with Heat and Mass Transfer

  • Research Paper
  • Published:
Iranian Journal of Science and Technology, Transactions A: Science Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

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

    Article  MathSciNet  MATH  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  MATH  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    MathSciNet  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Hayat T, Noreen S (2010) Peristaltic transport of fourth grade fluid with heat transfer and induced magnetic field. CR Mec 338:518–528

    Article  MATH  Google Scholar 

  • 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

    Article  MathSciNet  MATH  Google Scholar 

  • 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

    Article  MATH  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  MathSciNet  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  MathSciNet  Google Scholar 

  • 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

    Article  Google Scholar 

  • Nadeem S, Akram S (2010a) Peristaltic flow of a Williamson fluid in an asymmetric channel. Commun Nonlinear Sci Numer Simul 15:1705–1716

    Article  MathSciNet  MATH  Google Scholar 

  • 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

    Article  MathSciNet  MATH  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  MathSciNet  MATH  Google Scholar 

  • Radhakrishnamacharya G, Srinivasulu Ch (2007) Influence of wall properties on peristaltic transport with heat transfer. CR Mec 335:369–373

    Article  MATH  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  MathSciNet  MATH  Google Scholar 

  • Srinivas S, Pushparaj V (2008) Non-linear peristaltic transport in an inclined asymmetric channel. Commun Nonlinear Sci Numer Simul 13:1782–1795

    Article  Google Scholar 

  • Tripathi D (2011) Peristaltic transport of a viscoelastic fluid in a channel. Acta Astronaut 68:1379–1385

    Article  Google Scholar 

  • Tripathi D (2012) Peristaltic hemodynamic flow of couple stress fluids through a porous medium with slip effect. Transp Porous Media 92:559–572

    Article  MathSciNet  Google Scholar 

  • Tripathi D (2013) Study of transient peristaltic heat flow through a finite porous channel. Math Comput Model 57:1270–1283

    Article  MathSciNet  Google Scholar 

  • 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

    Article  MathSciNet  MATH  Google Scholar 

  • 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

    Article  MathSciNet  Google Scholar 

  • 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

    Article  Google Scholar 

Download references

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

  1. Department of Mathematics, Lovely Professional University, Phagwara, Punjab, 144411, India

    K. Ramesh

  2. Department of Mathematics, Visvesvaraya National Institute of Technology, Nagpur, 440010, India

    M. Devakar

Authors
  1. K. Ramesh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Devakar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Devakar.

Appendix

Appendix

$$A_{1} = 1/(h_{2} - h_{1} ) + \beta (h_{1} + h_{2} )/2;$$
$$A_{2} = \beta h_{1}^{2} /2 - A_{1} h_{1} ;$$
$$B_{1} = 1/(h_{2} - h_{1} ) - ScSr\beta (h_{1} + h_{2} )/2;$$
$$B_{2} = - ScSr\beta h_{1}^{2} /2 - B_{1} h_{1} ;$$
$$C_{1} = D_{1} + C_{2} D_{2} ;$$
$$C_{2} = D_{5} /D_{6} ;$$
$$C_{3} = (GcScSr\beta - Gr\beta )/6m_{1}^{2} ;$$
$$C_{4} = (GcB_{1} + GrA_{1} )/2m_{1}^{2} ;$$
$$C_{5} = D_{3} + C_{2} D_{4} ;$$
$$C_{6} = F/2 - C_{1} \cosh (m_{1} h_{1} ) - C_{2} \sinh (m_{1} h_{1} ) - C_{3} h_{1}^{3} - C_{4} h_{1}^{2} - C_{5} h_{1} ;$$
$$D_{1} = (3C_{3} (h_{1}^{2} - h_{2}^{2} ) + 2C_{4} (h_{1} - h_{2} ))/m_{1} (\sinh (m_{1} h_{2} ) - \sinh (m_{1} h_{1} ));$$
$$D_{2} = C_{2} (\cosh (m_{1} h_{1} ) - \cosh (m_{1} h_{2} ))/(\sinh (m_{1} h_{2} ) - \sinh (m_{1} h_{1} ));$$
$$D_{3} = - (1 + D_{1} m_{1} \sinh (m_{1} h_{1} ) + 3C_{3} h_{1}^{2} + 2C_{4} h_{1} );$$
$$D_{4} = - (m_{1} \cosh (m_{1} h_{1} ) + D_{2} m_{1} \sinh (m_{1} h_{1} ));$$
$$D_{5} = F - D_{1} (\cosh (m_{1} h_{1} ) - \cosh (m_{1} h_{2} )) - C_{3} (h_{1}^{3} - h_{2}^{3} ) - C_{4} (h_{1}^{2} - h_{2}^{2} ) - D_{3} (h_{1} - h_{2} );$$
$$D_{6} = D_{2} (\cosh (m_{1} h_{1} ) - \cosh (m_{1} h_{2} )) + (\sinh (m_{1} h_{1} ) - \sinh (m_{1} h_{2} )) + D_{4} (h_{1} - h_{2} );$$
$$E_{1} = G_{2} + E_{2} G_{3} ;$$
$$E_{2} = G_{6} /G_{7} ;$$
$$E_{3} = m_{1}^{4} (C_{1}^{3} + 3C_{1} C_{2}^{2} )/32;$$
$$E_{4} = m_{1}^{4} (C_{2}^{3} + 3C_{2} C_{1}^{2} )/32;$$
$$E_{5} = 4m_{1} (m_{1} C_{1}^{2} C_{4} + m_{1} C_{2}^{2} C_{4} - 2C_{1} C_{2} C_{3} );$$
$$E_{6} = 4m_{1} ( - m_{1} C_{1}^{2} C_{3} - m_{1} C_{2}^{2} C_{3} + 2C_{1} C_{2} C_{4} );$$
$$E_{7} = 3m_{1}^{2} C_{3} (C_{1}^{2} + C_{2}^{2} );$$
$$E_{8} = 6m_{1}^{2} C_{1} C_{2} C_{3} ;$$
$$E_{9} = ( - 3m_{1}^{6} C_{2}^{3} + 3m_{1}^{6} C_{1}^{2} C_{2} + 216C_{2} C_{3}^{2} - 144m_{1} C_{1} C_{3} C_{4} + 48m_{1}^{2} C_{2} C_{4}^{2} )/8m_{1} ;$$
$$E_{10} = (3m_{1}^{6} C_{1}^{3} - 3m_{1}^{6} C_{2}^{2} C_{1} + 216C_{1} C_{3}^{2} - 144m_{1} C_{2} C_{3} C_{4} + 48m_{1}^{2} C_{1} C_{4}^{2} )/8m_{1} ;$$
$$E_{11} = 18m_{1} C_{2} C_{3} C_{4} - 27C_{1} C_{3}^{2} ;$$
$$E_{12} = 18m_{1} C_{1} C_{3} C_{4} - 27C_{2} C_{3}^{2} ;$$
$$E_{13} = 18m_{1} C_{2} C_{3}^{2} ;$$
$$E_{14} = 18m_{1} C_{1} C_{3}^{2} ;$$
$$E_{15} = - 216C_{1}^{3} /m_{1}^{2} ;$$
$$E_{16} = - 216C_{3}^{2} C_{4} /m_{1}^{2} ;$$
$$E_{17} = G_{4} + E_{2} G_{5} ;$$
$$\begin{aligned} E_{18} & = - (E_{1} \cosh (m_{1} h_{1} ) + E_{2} \sinh (m_{1} h_{1} ) + E_{3} \cosh (3m_{1} h_{1} ) + E_{4} \sinh (3m_{1} h_{1} ) \\ & \quad + E_{5} \cosh (2m_{1} h_{1} ) + E_{6} \sinh (2m_{1} h_{1} ) \\ & \quad + E_{7} h_{1} \cosh (2m_{1} h_{1} ) \\ & \quad + E_{8} h_{1} \sinh (2m_{1} h_{1} ) + E_{9} h_{1} \cosh (m_{1} h_{1} ) + E_{10} h_{1} \sinh (m_{1} h_{1} ) \\ & \quad + E_{11} h_{1}^{2} \cosh (m_{1} h_{1} ) \\ & \quad + E_{12} h_{1}^{2} \sinh (m_{1} h_{1} ) \\ & \quad + E_{13} h_{1}^{3} \cosh (m_{1} h_{1} ) + E_{14} h_{1}^{3} \sinh (m_{1} h_{1} ) + E_{15} h_{1}^{3} + E_{16} h_{1}^{2} + E_{17} h_{1} ); \\ \end{aligned}$$
$$F_{1} = (ScSr\beta - Gr\beta - 6m_{1}^{2} C_{3} )/2;$$
$$F_{2} = GrA_{1} + GcB_{1} - 2m_{1}^{2} C_{4} ;$$
$$F_{3} = GrA_{2} + GcB_{2} - m_{1}^{2} (1 + C_{5} ) + 6C_{3} ;$$
$$F_{4} = - 12m_{1}^{3} C_{1} C_{4}^{2} - 72m_{1}^{2} C_{2} C_{3} C_{4} + 2m_{1}^{2} E_{10} + 6m_{1} E_{11} + 6E_{14} ;$$
$$F_{5} = - 12m_{1}^{3} C_{2} C_{4}^{2} - 72m_{1}^{2} C_{1} C_{3} C_{4} + 2m_{1}^{2} E_{9} + 6m_{1} E_{12} + 6E_{13} ;$$
$$F_{6} = m_{1}^{2} (6m_{1} E_{5} + 11E_{8} );$$
$$F_{7} = m_{1}^{2} (6m_{1} E_{6} + 11E_{7} );$$
$$F_{8} = 24m_{1}^{3} E_{3} ;$$
$$F_{9} = 24m_{1}^{3} E_{4} ;$$
$$F_{10} = 4m_{1}^{2} E_{12} + 18m_{1} E_{13} - 216m_{1}^{2} C_{2} C_{3}^{2} - 72m_{1}^{3} C_{1} C_{3} C_{4} ;$$
$$F_{11} = 4m_{1}^{2} E_{11} + 18m_{1} E_{14} - 216m_{1}^{2} C_{1} C_{3}^{2} - 72m_{1}^{3} C_{2} C_{3} C_{4} ;$$
$$F_{12} = 6m_{1}^{3} E_{7} ;$$
$$F_{13} = 6m_{1}^{3} E_{8} ;$$
$$F_{14} = 6m_{1}^{2} (E_{14} - 18m_{1} C_{1} C_{3}^{2} );$$
$$F_{15} = 6m_{1}^{2} (E_{13} - 18m_{1} C_{2} C_{3}^{2} );$$
$$F_{16} = - 6m_{1}^{4} (3C_{2}^{2} C_{3} + 2m_{1} C_{1} C_{2} C_{4} );$$
$$F_{17} = - 6m_{1}^{4} (3C_{1}^{2} C_{3} + 2m_{1} C_{1} C_{2} C_{4} );$$
$$F_{18} = - 3m_{1}^{7} C_{1} C_{2}^{2} ;$$
$$F_{19} = - 3m_{1}^{7} C_{2} C_{1}^{2} ;$$
$$F_{20} = - 36m_{1}^{5} C_{1} C_{2} C_{3} ;$$
$$F_{21} = - 12m_{1}^{4} (m_{1} C_{1}^{2} C_{4} + 3C_{1} C_{2} C_{3} + m_{1} C_{2}^{2} C_{4} );$$
$$F_{22} = - 3m_{1}^{7} (C_{2}^{3} + 2C_{1}^{2} C_{2} );$$
$$F_{23} = - 3m_{1}^{7} (C_{1}^{3} + 2C_{2}^{2} C_{1} );$$
$$F_{24} = - 36m_{1}^{5} (C_{1}^{2} C_{3} + C_{2}^{2} C_{3} );$$
$$F_{25} = - 3(m_{1}^{2} E_{15} + 216C_{3}^{3} );$$
$$F_{26} = - 2(m_{1}^{2} E_{16} + 216C_{3}^{2} C_{4} );$$
$$F_{27} = 6E_{15} - 72C_{2} C_{4}^{2} - m_{1}^{2} E_{17} ;$$
$$\begin{aligned} G_{1} & = 3m_{1} E_{1} (\sinh (3m_{1} h_{1} ) - \sinh (3m_{1} h_{2} )) + 3m_{1} E_{4} (\cosh (3m_{1} h_{1} ) - \cosh (3m_{1} h_{2} )) \\ & \quad + (2m_{1} E_{5} + E_{8} ) (\sinh (2m_{1} h_{1} ) - \sinh (2m_{1} h_{2} )) \\ & \quad + (2m_{1} E_{6} + E_{7} )(\cosh (2m_{1} h_{1} ) - \cosh (2m_{1} h_{2} )) + E_{10} (\sinh (m_{1} h_{1} ) - \sinh (m_{1} h_{2} )) \\ & \quad + E_{9} (\cosh (m_{1} h_{1} ) - \cosh (m_{1} h_{2} )) \\ & \quad + 2m_{1} E_{7} (h_{1} \sinh (2m_{1} h_{1} ) - h_{2} \sinh (2m_{1} h_{2} )) \\ & \quad + 2m_{1} E_{8} (h_{1} \cosh (2m_{1} h_{1} ) - h_{2} \cosh (2m_{1} h_{2} )) \\ & \quad + (m_{1} E_{9} + 2E_{12} ) (h_{1} \sinh (m_{1} h_{1} ) - h_{2} \sinh (m_{1} h_{2} )) \\ & \quad + (m_{1} E_{10} + 2E_{11} )(h_{1} \cosh (m_{1} h_{1} ) - h_{2} \cosh (m_{1} h_{2} )) \\ & \quad + (m_{1} E_{11} + 3E_{14} )(h_{1}^{2} \sinh (m_{1} h_{1} ) - h_{2}^{2} \sinh (m_{1} h_{2} )) \\ & \quad + (m_{1} E_{12} + 3E_{13} )(h_{1}^{2} \cosh (m_{1} h_{1} ) - h_{2}^{2} \cosh (m_{1} h_{2} )) \\ & \quad + m_{1} E_{13} (h_{1}^{3} \sinh (m_{1} h_{1} ) - h_{2}^{3} \sinh (m_{1} h_{2} )) \\ & \quad + m_{1} E_{14} (h_{1}^{3} \cosh (m_{1} h_{1} ) - h_{2}^{3} \cosh (m_{1} h_{2} )) + 3E_{15} (h_{1}^{2} - h_{2}^{2} ) + 2E_{16} (h_{1} - h_{2} ); \\ \end{aligned}$$
$$G_{2} = (\cosh (m_{1} h_{2} ) - \cosh (m_{1} h_{1} ))/(\sinh (m_{1} h_{1} ) - \sinh (m_{1} h_{2} ));$$
$$G_{3} = G_{1} /m_{1} (\sinh (m_{1} h_{2} ) - \sinh (m_{1} h_{1} ));$$
$$\begin{aligned} G_{4} & = - (m_{1} G_{2} \sinh (m_{1} h_{1} ) + 3m_{1} E_{3} \sinh (3m_{1} h_{1} ) + 3m_{1} E_{4} \cosh (3m_{1} h_{1} ) + (2m_{1} E_{5 } + E_{8} )\sinh (2m_{1} h_{1} ) \\ & \quad + (2m_{1} E_{6} + E_{7} )\cosh (2m_{1} h_{1} ) + E_{10} \sinh (m_{1} h_{1} ) + E_{9} \cosh (m_{1} h_{1} ) \\ & \quad + 2m_{1} E_{7 } h_{1} \sinh (2m_{1} h_{1} ) + 2m_{1} E_{8 } h_{1} \cosh (2m_{1} h_{1} ) + (m_{1} E_{9} + 2E_{12} )h_{1} \sinh (m_{1} h_{1} ) \\ & \quad + (m_{1} E_{10} + 2E_{11} )h_{1} \cosh (m_{1} h_{1} ) + (m_{1} E_{11} + 3E_{14} )h_{1}^{2} \sinh (m_{1} h_{1} ) \\ & \quad + (m_{1 } E_{12} + 3E_{13} )h_{1}^{2} \cosh (m_{1} h_{1} ) + m_{1} E_{13 } h_{1}^{3} \sinh (m_{1} h_{1} ) + m_{1} E_{14 } h_{1}^{3} \cosh (m_{1} h_{1} ) + 3E_{15} h_{1}^{2} ); \\ \end{aligned}$$
$$G_{5} = G_{3} \sinh (m_{1} h_{1} ) + m_{1} \cosh (m_{1} h_{1} );$$
$$\begin{aligned} G_{6} & = G_{2} (\cosh (m_{1} h_{2} ) - \cosh (m_{1} h_{1} )) + E_{4} (\sinh (3m_{1} h_{2} ) - \sinh (3m_{1} h_{1} )) + E_{3} (\cosh (3m_{1} h_{2} ) - \cosh (3m_{1} h_{1} )) \\ & \quad + E_{6} (\sinh (2m_{1} h_{2} ) - \sinh (2m_{1} h_{1} )) + E_{5} (\cosh (2m_{1} h_{2} ) - \cosh (2m_{1} h_{1} )) \\ & \quad + E_{8} (h_{2} \sinh (2m_{1} h_{2} ) - h_{1} \sinh (2m_{1} h_{1} )) + E_{7} (h_{2} \cosh (2m_{1} h_{2} ) - h_{1} \cosh (2m_{1} h_{1} )) \\ & \quad + E_{10} (h_{2} \sinh (m_{1} h_{2} ) - h_{1} \sinh (m_{1} h_{1} )) + E_{9} (h_{2} \cosh (m_{1} h_{2} ) - h_{1} \cosh (m_{1} h_{1} )) \\ & \quad + E_{12} (h_{2}^{2} \sinh (m_{1} h_{2} ) - h_{1}^{2} \sinh (m_{1} h_{1} )) + E_{11} (h_{2}^{2} \cosh (m_{1} h_{2} ) - h_{1}^{2} \cosh (m_{1} h_{1} )) \\ & \quad + E_{14} (h_{2}^{3} \sinh (m_{1} h_{2} ) - h_{1}^{3} \sinh (m_{1} h_{1} )) + E_{13} (h_{2}^{3} \cosh (m_{1} h_{2} ) - h_{1}^{3} \cosh (m_{1} h_{1} )) \\ & \quad + E_{15} (h_{2}^{3} - h_{1}^{3} ) + E_{16} (h_{2}^{2} - h_{1}^{2} ) + G_{4} (h_{2} - h_{1} ); \\ \end{aligned}$$
$$G_{7} = G_{3} (\cosh (m_{1} h_{1} ) - \cosh (m_{1} h_{2} )) + (\sinh (m_{1} h_{1} ) - \sinh (m_{1} h_{2} )) + G_{5} (h_{1} - h_{2} ).$$

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40995-017-0193-1

Keywords

Search

Navigation