Numerical investigation for peristaltic flow of Carreau–Yasuda magneto-nanofluid with modified Darcy and radiation

  • T. Hayat
  • Bilal AhmedEmail author
  • F. M. Abbasi
  • A. Alsaedi


This paper reports numerical study for peristalsis of Carreau–Yasuda nanofluid in a symmetric channel. Constant magnetic field is applied. Modified Darcy’s law and nonlinear thermal radiation effects are considered. Viscous dissipation and Ohmic heating effects are also present. Long wavelength and small Reynolds number are considered. Resulting nonlinear problems are solved numerically. Graphical illustrations depict that temperature increases for larger Hartmann number and it decays for thermophoresis parameter.


Peristalsis Carreau–Yasuda fluid Nanoparticles Magnetic field Darcy’s law Nonlinear thermal radiation 



This project was funded by the Deanship of Scientific Research (DSR) King Abdulaziz University, Jeddah, Saudi Arabia under Grant No. (RG-27-130-39). The authors, therefore acknowledge with thanks DSR technical and financial support.


  1. 1.
    Choi SUS. Enhancing thermal conductivity of fluids with nanoparticles. ASME Fluids Eng Div. 1995;231:99–105.Google Scholar
  2. 2.
    Brinkman HC. The viscosity of concentrated suspensions and solutions. J Chem Phys. 1952;20:571–81.CrossRefGoogle Scholar
  3. 3.
    Liu Z, Yan Y, Fu R, Alsaady M. Enhancement of solar energy collection with magnetic nanofluids. Therm Sci Eng Prog. 2018;8:130–5.CrossRefGoogle Scholar
  4. 4.
    Sheikholeslami M, Shehzad SA, Li Z, Shafee A. Numerical modeling for alumina nanofluid magnetohydrodynamic convective heat transfer in a permeable medium using Darcy law. Int J Heat Mass Transf. 2018;127:614–22.CrossRefGoogle Scholar
  5. 5.
    Nayak RK, Bhattacharyya S, Pop I. Effects of nanoparticles dispersion on the mixed convection of a nanofluid in a skewed enclosure. Int J Heat Mass Transf. 2018;125:908–19.CrossRefGoogle Scholar
  6. 6.
    Chon CH, Kihm KD, Lee SP, Choi SUS. Empirical correlation finding the role of temperature and particle size for nanofluid Al2O3 thermal conductivity enhancement. Appl Phys Lett. 2005;87:153107.CrossRefGoogle Scholar
  7. 7.
    Sharifi I, Shokrollahi H, Amiri S. Ferrite-based magnetic nanofluids used in hyperthermia applications. J Magn Magn Mater. 2012;324:903–15.CrossRefGoogle Scholar
  8. 8.
    Majeed A, Zeeshan A, Alamri SZ, Ellahi R. Heat transfer analysis in ferromagnetic viscoelastic fluid flow over a stretching sheet with suction. Neural Comput Appl. 2018;30:1947–55.CrossRefGoogle Scholar
  9. 9.
    Hassan M, Marin M, Ellahi R, Alamri SZ. Exploration of convective heat transfer and flow characteristics synthesis by Cu–Ag/water hybrid-nanofluids. Heat Transf Res. 2018;49:1837–48.CrossRefGoogle Scholar
  10. 10.
    Hamilton RL, Crosser OK. Thermal conductivity of heterogeneous two component systems. EC Fundam. 1962;1:187–91.CrossRefGoogle Scholar
  11. 11.
    Hayat T, Ahmed B, Abbasi FM, Alsaedi A. Hydromagnetic peristalsis of water based nanofluids with temperature dependent viscosity: a comparative study. J Mol Liq. 2017;234:324–9.CrossRefGoogle Scholar
  12. 12.
    Zhang C, Zheng L, Zhang X, Chen G. MHD flow and radiation heat transfer of nanofluids in porous media with variable surface heat flux and chemical reaction. Appl Math Model. 2015;39:165–81.CrossRefGoogle Scholar
  13. 13.
    Bhatti MM, Zeeshan A, Ellahi R, Shit GC. Mathematical modeling of heat and mass transfer effects on MHD peristaltic propulsion of two-phase flow through a Darcy–Brinkman–Forchheimer porous medium. Adv Powder Technol. 2018;29:1189–97.CrossRefGoogle Scholar
  14. 14.
    Sheikholeslami M, Hayat T, Alsaedi A. Numerical simulation of nanofluid forced convection heat transfer improvement in existence of magnetic field using lattice Boltzmann method. Int J Heat Mass Transf. 2017;108:1870–83.CrossRefGoogle Scholar
  15. 15.
    Hassan M, Marin M, Alsharif A, Ellahi R. Convection heat transfer flow of nanofluid in a porous medium over wavy surface. Phys Lett A. 2018;382:2749–53.CrossRefGoogle Scholar
  16. 16.
    Hayat T, Aziz A, Muhammad T, Ahmad B. Influence of magnetic field in three-dimensional flow of couple stress nanofluid over a nonlinearly stretching surface with convective condition. PLoS ONE. 2015;10:e0145332.CrossRefGoogle Scholar
  17. 17.
    Hayat T, Aziz A, Muhammad T, Alsaedi A. On model for flow of Burgers nanofluid with Cattaneo–Christov double diffusion. Chin J Phys. 2017;55:916–29.CrossRefGoogle Scholar
  18. 18.
    Khan AA, Masood F, Ellahi R, Bhatti MM. Mass transport on chemicalized fourth-grade fluid propagating peristaltically through a curved channel with magnetic effects. J Mol Liq. 2018;258:186–95.CrossRefGoogle Scholar
  19. 19.
    Hayat T, Muhammad K, Alsaedi A, Asghar S. Numerical study for melting heat transfer and homogeneous-heterogeneous reactions in flow involving carbon nanotubes. Results Phys. 2018;8:415–21.CrossRefGoogle Scholar
  20. 20.
    Hayat T, Ijaz Khan M, Waqas M, Alsaedi A, Imran Khan M. Radiative flow of micropolar nanofluid accounting thermophoresis and Brownian moment. Int J Hydrogen Energy. 2017;42:16821–33.CrossRefGoogle Scholar
  21. 21.
    Ellahi R, Alamri SZ, Basit A, Majeed A. Effects of MHD and slip on heat transfer boundary layer flow over a moving plate based on specific entropy generation. J Taibah Univ Sci. 2018;12:476–82.CrossRefGoogle Scholar
  22. 22.
    Mahian O, Kolsi L, Amani M, Estelle P, Ahmadi G, Kleinstreuer C, Marshall JS, Siavashi M, Taylor RA, Niazmand H, Wongwises S, Hayat T, Kolanjiyil A, Kasaeian A, Pop I. Recent advances in modelling and simulation of nanofluid flows-part I: fundamentals and theory. Phys Rep. 2018. Scholar
  23. 23.
    Mahian O, Kolsi L, Amani M, Estelle P, Ahmadi G, Kleinstreuer C, Marshall JS, Siavashi M, Taylor RA, Abu-Nada E, Rashidi S, Niazmand H, Wongwises S, Hayat T, Kolanjiyil A, Kasaeian A, Pop I. Recent advances in modelling and simulation of nanofluid flows-part II: applications. Phys Rep. 2018. Scholar
  24. 24.
    Hayat T, Hussain Z, Muhammad T, Alsaedi A. Effects of homogeneous and heterogeneous reactions in flow of nanofluids over a nonlinear stretching surface with variable surface thickness. J Mol Liq. 2018;221:1121–7.CrossRefGoogle Scholar
  25. 25.
    Hayat T, Ahmed B, Alsaedi A, Abbasi FM. Numerical study for peristalsis of Carreau–Yasuda nanomaterial with convective and zero mass flux condition. Result Phys. 2018;8:1168–77.CrossRefGoogle Scholar
  26. 26.
    Ali N, Sajid M, Javed T, Abbas Z. Heat transfer analysis of peristaltic flow in a curved channel. Int J Heat Mass Transf. 2017;53:3319–25.CrossRefGoogle Scholar
  27. 27.
    Tanveer A, Hayat T, Alsaadi F, Alsaedi A. Mixed convection peristaltic flow of Eyring–Powell nanofluid in a curved channel with compliant walls. Comput Biol Med. 2017;82:71–9.CrossRefGoogle Scholar
  28. 28.
    Ali N, Javid K, Sajid M, Zaman A, Hayat T. Numerical simulation of Oldroyd 8-constant fluid flow and heat transfer in a curved channel. Int J Heat Mass Transf. 2016;94:500–8.CrossRefGoogle Scholar
  29. 29.
    Zeeshan A, Ijaz N, Abbas T, Ellahi R. The sustainable characteristic of bio-bi-phase flow of peristaltic transport of MHD Jeffery fluid in human body. Sustainability. 2018;10:1–17.CrossRefGoogle Scholar
  30. 30.
    Hayat T, Bilal Ahmed FM, Abbasi B Ahmad. Mixed convective peristaltic flow of carbon nanotubes submerged in water using different thermal conductivity models. Comput Methods Programs Biomed. 2016;135:141–50.CrossRefGoogle Scholar
  31. 31.
    Sisko AW. The flow of lubricating greases. Ind Eng Chem. 1958;50:1789–92.CrossRefGoogle Scholar
  32. 32.
    Maxwell JC. On the dynamical theory of gases. Philos Trans R Soc Lond. 1867;157:49–88.CrossRefGoogle Scholar
  33. 33.
    Oldroyd JG. On the formulation of rheological equations of state. Proc R Soc A Math Phys Eng Sci. 1950;200:523–41.Google Scholar
  34. 34.
    Carreau PJ. Rheological equations from molecular network theories. J Rheol. 1972;16:99–127.Google Scholar
  35. 35.
    Abbasi FM, Hayat T, Alsaedi A. Numerical analysis for MHD peristaltic transport of Carreau–Yasuda fluid in a curved channel with Hall effects. J Magn Magn Mater. 2015;382:104–10.CrossRefGoogle Scholar
  36. 36.
    Buongiorno J. Convective transport in nanofluids. ASME J Heat Transf. 2006;128:240–50.CrossRefGoogle Scholar
  37. 37.
    Abbasi FM, Hayat T, Shehzad SA, Alsaadi F, Altoaibi N. Hydromagnetic peristaltic transport of copper–water nanofluid with temperature-dependent effective viscosity. Particuology. 2016;27:133–40.CrossRefGoogle Scholar
  38. 38.
    Shehzad SA, Abbasi FM, Hayat T, Alsaadi F, Mousa G. Peristalsis in a curved channel with slip condition and radial magnetic field. Int J Heat Mass Transf. 2015;91:562–9.CrossRefGoogle Scholar
  39. 39.
    Abbasi FM, Hayat T, Alsaedi A. Peristaltic transport of magneto-nanoparticles submerged in water: model for drug delivery system. Phys E. 2015;68:123–32.CrossRefGoogle Scholar
  40. 40.
    Abbasi FM, Hayat T, Ahmad B. Peristaltic transport of copper–water nanofluid saturating porous medium. Phys E. 2015;67:47–53.CrossRefGoogle Scholar
  41. 41.
    Darcy H. Les Fontaines Publiques De La Ville De Dijon. Paris: Dalmont; 1856. p. 647.Google Scholar
  42. 42.
    Tanveer A, Hayat T, Alsaedi A, Ahmad B. On modified Darcy’s law utilization in peristalsis of Sisko fluid. J Mol Liq. 2017;236:290–7.CrossRefGoogle Scholar
  43. 43.
    Tan WC, Masuoka T. Stokes’ first problem for a second grade fluid in a porous half-space with heated boundary. Int J Non Linear Mech. 2005;40:515–22.CrossRefGoogle Scholar
  44. 44.
    Ul Haq R, Nadeem S, Khan ZH, Akbar NS. Thermal radiation and slip effects on MHD stagnation point flow of nanofluid over a stretching sheet. Phys E. 2015;65:17–23.CrossRefGoogle Scholar
  45. 45.
    Shehzad SA, Abbasi FM, Hayat T, Alsaadi F. MHD mixed convective peristaltic motion of nanofluid with joule heating and thermophoresis effects. PLoS ONE. 2014;9:e111417.CrossRefGoogle Scholar
  46. 46.
    Srinivas S, Kothandapani M. Peristaltic transport in an asymmetric channel with heat transfer—a note. Int Commun Heat Mass Transf. 2008;35:514–22.CrossRefGoogle Scholar
  47. 47.
    Sucharitha G, Lakshminarayana P, Sandeep N. Joule heating and wall flexibility effects on the peristaltic flow of magnetohydrodynamic nanofluid. Int J Mech Sci. 2017;131–132:52–62.CrossRefGoogle Scholar
  48. 48.
    Hayat T, Abbasi FM, Alsaedi A, Alsaadi F. Hall and Ohmic heating effects on the peristaltic transport of a Carreau–Yasuda fluid in an asymmetric channel. Z Naturforsch. 2014;69a:43–51.Google Scholar
  49. 49.
    Xuan Y, Li Q. Heat transfer enhancement of nanofuids. Int J Heat Fluid Flow. 2000;21:58–64.CrossRefGoogle Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2019

Authors and Affiliations

  • T. Hayat
    • 1
    • 2
  • Bilal Ahmed
    • 1
    Email author
  • F. M. Abbasi
    • 3
  • A. Alsaedi
    • 3
  1. 1.Department of MathematicsQuaid-I-Azam UniversityIslamabadPakistan
  2. 2.Faculty of Science, Nonlinear Analysis and Applied Mathematics (NAAM) Research GroupKing Abdulaziz UniversityJeddahSaudi Arabia
  3. 3.Department of MathematicsCOMSATS Institute of Information TechnologyIslamabadPakistan

Personalised recommendations