Multiple nature analysis of Carreau nanomaterial flow due to shrinking geometry with heat transfer

Original Article


An astonishing feature of modern research in the field of fluid flow and heat transfer is the suspension of small solid particles (nanoparticle) in the working fluid to increase the low thermal conductivity of these fluids. Because of unique chemical and physical properties, nanomaterials are being progressively utilized in almost every field of science and technology. Therefore, the intent of current manuscript is to theoretically examine the magneto-hydrodynamic flow of Carreau nanofluids along with heat transport in the presence of heat generation driven by a wedge-shaped shrinking geometry. We incorporated the revised Buongiorno’s model in which nanofluids particle fraction on the boundary is passively controlled. Mathematical modeling of assumed physical problem results in a system of non-linear partial differential equations outlining the basic conservation laws. The governing problem is made dimensionless with the assistance of non-dimensional variables and numerical solutions are computed via a built-in MATLAB solver bvp4c. The computed results showed that multiple solutions (first and second) exist for the non-dimensional velocity, temperature and concentration distributions by applying the said numerical scheme. We concluded that by enhancing the magnetic parameter the nanofluid velocity increases in case of second solution while an opposite is true for temperature. Further, the outcomes indicate that higher heat generation parameter leads to enhance the temperature distributions in both solutions.


Carreau nanofluid Multiple solutions Heat generation/absorption Wedge-shape geometry Magnetic field 



  1. Akbar NS, Nadeem S, Haq RU, Ye S (2014) MHD stagnation point flow of Carreau fluid toward a permeable shrinking sheet: dual solutions. Ain Shams Eng J 5(4):1233–1239CrossRefGoogle Scholar
  2. Awaludin IS, Ishak A, Pop I (2018) On the stability of MHD boundary layer flow over a stretching/shrinking wedge. Sci Rep 8:13622CrossRefGoogle Scholar
  3. Boyd ID, Martin MJ (2010) Falkner-Skan flow over a wedge with slip boundary conditions. J Thermophys Heat Transf 24(2):263–270CrossRefGoogle Scholar
  4. Buongiorno J (2006) Convective transport in nanofluids. J Heat Transf 128:240–250CrossRefGoogle Scholar
  5. Choi SUS (1995) Enhancing thermal conductivity of fluids with nanoparticles. ASME-Publications-Fed 231:99–106Google Scholar
  6. Falkner VM, Skan SW (1931) Some approximate solutions of the boundary-layer for flow past a stretching boundary. SIAM J Appl Math 46:1350–1358Google Scholar
  7. Hamid A, Hashim MK, Alghamd M (2019) MHD Blasius flow of radiative Williamson nanofluid over a vertical plate. Int J Modern Phys B 33:1950245CrossRefGoogle Scholar
  8. Hartree DR (1937) On equation occurring in Falkner and Skan’s approximate treatment of the equations of the boundary layer. Proc Cambridge Philos Soc 33:323–329Google Scholar
  9. Ibrahim W, Tulu A (2019) Magnetohydrodynamic (MHD) boundary layer flow past a wedge with heat transfer and viscous effects of nanofluid embedded in porous media. Math Prob Eng 450:7852. CrossRefGoogle Scholar
  10. Ishak A, Nazar R, Pop I (2007) Falkner-Skan equation for flow past a moving wedge with suction or injection. J Appl Math Comput 25:67–83CrossRefGoogle Scholar
  11. Ishaq A, Nazar R, Pop I (2008) MHD boundary-layer flow of a micropolar fluid past a wedge with variable wall temperature. Acta Mech 196:75–86CrossRefGoogle Scholar
  12. Khan M, Hafeez AA (2017) A review on slip-flow and heat transfer performance of nanofluids from a permeable shrinking surface with thermal radiation: dual solutions. Chem Eng Sci 173:1–11CrossRefGoogle Scholar
  13. Khan WA, Pop I (2010) Boundary-layer flow of a nanofluid past a stretching sheet. Int J Heat Mass Transf 53:2477–2483CrossRefGoogle Scholar
  14. Khan U, Ahmed N, Mohyud-Din ST (2018) Analysis of magneto hydrodynamic flow and heat transfer of Cu-water nanofluid between parallel plates for different shapes of nanoparticles. Neural Comput Appl 29(10):695–703CrossRefGoogle Scholar
  15. Lee S, Choi SUS, Li S, Eastman JA (1999) Measuring thermal conductivity of fluids containing oxide nanoparticles. J Heat Transf 121:280–289CrossRefGoogle Scholar
  16. Ma Y, Mohebbi R, Rashidi MM, Yang Z (2019) MHD convective heat transfer of Ag–Mg/water hybrid nanofluid in a channel with active heaters and coolers. Int J Heat Mass Transf 137:714–726CrossRefGoogle Scholar
  17. Mabood F, Khan WA, Ismail AIM (2015) MHD boundary layer flow and heat transfer of nanofluids over a nonlinear stretching sheet: a numerical study. J Mag Mag Mater 374:569–576CrossRefGoogle Scholar
  18. Mutuku-Njane WN, Makinde OD (2014) On hydromagnetic boundary layer flow of nanofluids over a permeable moving surface with Newtonian heating. Latin Am Appl Res 44:57–62Google Scholar
  19. Reddy NA, Raju MC, Varma SVK (2009) Thermo diffusion and chemical effects with simultaneous thermal and mass diffusion in MHD mixed convection flow with Ohmic heating. J Naval Archit Mar Eng 6:84–93CrossRefGoogle Scholar
  20. Sayyed SR, Singh BB, Bano N (2018) Analytical solution of MHD slip flow past a constant wedge within porous medium using DTM-Pade. Appl Math Comput 321:472–482Google Scholar
  21. Sheikholeslami M, Bandpy MG, Ganji DD (2013) Numerical investigation of MHD effect on Al2O3-nanofluid flow and heat transfer in a semi-annulus enclosure using LBM. Energy 1(60):501–510CrossRefGoogle Scholar
  22. Wang CW (2007) Stagnation flow towards a shrinking sheet. Int J Nonlinear Mech 43(5):377–382CrossRefGoogle Scholar
  23. Xu X, Chen S (2017) Dual solutions of a boundary layer problem for MHD nanofluids through a permeable wedge with variable viscosity. Boundary Val Prob 147Google Scholar
  24. Yih KA (1999) MHD forced convection flow adjacent to a non-isothermal wedge. Int Commun Heat Mass Transf 26(6):819–827CrossRefGoogle Scholar

Copyright information

© King Abdulaziz City for Science and Technology 2019

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsRiphah International UniversityIslamabadPakistan

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