, Volume 9, Issue 2, pp 483–494 | Cite as

Comparative Study on MHD CARREAU Fluid Due to Stretching/Shrinking Surface in Suspension of Dust and Graphene Nanoparticles

  • H. B. Santhosh
  • Mahesha
  • S. Suresh Kumar RajuEmail author
  • C. S. K. Raju


In this investigation, we compared the effect of unsteady magneto hydrodynamic Carreau fluid in the interruption of graphene nanoparticles with heat generation over stretching and shrinking surface. The simulation is performed by combination of graphene nanoparticles into base water. Dispersion of graphene nanoparticles into base fluid finds several applications, such as biosensors, detection and purification of cancer cells, biocompatibility, and bio-imaging. The arising set of dimensional partial differential equations (PDEs) is converted into a set of non-dimensional ordinary differential equations (ODEs) by suitable similarity transformations, and then solved by the help of Runge-Kutta with shooting technique. The numerical results for non-dimensional velocity and temperature are displayed with graphs. We also analyzed the physical quantities (friction factor and local Nusselt number) for various values of non-dimensional physical parameters mathematically, and they are presented through tables. We also compared the present results with existing literature under some limited case. At the end of our analysis, we noted that radiation amplifies temperature profiles of both stretching and shrinking sheet cases. But, compared to shrinking sheet stretching sheet gains higher values. Heat generation parameter enriches temperature profiles in both stretching and shrinking sheets; compared to stretching sheet, shrinking sheet gains higher values.


Carreau fluid Heat generation parameter Radiation Stretching/shrinking sheet Porosity parameter Graphene nanoparticles 



The authors are grateful to the Deanship of Scientific Research at King Faisal University for the support under the grant 186046.


  1. 1.
    Nadeem, & Haque, R. U. (2012). MHD flow of a Casson fluid over an exponentially shrinking sheet. Scientia Iranica, 9(6), 1550–1553.CrossRefGoogle Scholar
  2. 2.
    kumari, A., & Padmavathi, K. (2017). Unsteady heat transfer flow of nano fluid over permeable shrinking sheet with viscous dissipation and connective boundary conditions. International Journal of Research in Advanced Engineering and Technology, 3(1), 14–21.Google Scholar
  3. 3.
    Zaimi, K. (2013). Flow and heat transfer over a shrinking sheet in a nano fluid with suction at the boundary. American Institute of Physics, 1571(1).Google Scholar
  4. 4.
    Wang, C. Y. (2013). Stagnation flow towards shrinking sheet. International Journal of Nonlinear Mechanics, 43(5), 377–382.CrossRefGoogle Scholar
  5. 5.
    Bachok, N., Aleng, N. L., Arifin, N. M., Ishak, A., & Senu, N. (2014). Fluid flow and heat transfer of nano fluid over a shrinking sheet., 8(9).Google Scholar
  6. 6.
    Bhattacharyya, K. (2011). Dual solution in unsteady stagnation-point flow over a shrinking sheet. Chinese Physics Letters, 28(8).Google Scholar
  7. 7.
    Akbar, N. S., Nadeem, S., Ul haq, R., & Shiwei, Y. (2014). MHD stagnation point flow of Carreau fluid toward a permeable shrinking sheet: dual solutions. Ain Shams Engineering Journal, 5(4), 1233–1239.CrossRefGoogle Scholar
  8. 8.
    Khan, M., Hashim, & AliSaleh, A. (2015). MHD stagnation-point flow of a Carreau fluid and heat transfer in the presence of convective boundary conditions. PLoS One, 11(6), 1–22.Google Scholar
  9. 9.
    Khan, M., & Hashim. (2015). Boundary layer flow and heat transfer to Carreau fluid over a nonlinear stretching sheet. AIP Advances, 5(10).Google Scholar
  10. 10.
    Khalid, A., Khan, I., Khan, A., & Shafi, S. (2015). Unsteady MHD free convection flow of Casson fluid past over an oscillating vertical plate embedded in a porous medium. Engineering Science and Technology, 18(3), 309–317.Google Scholar
  11. 11.
    Zaimi, K., Ishak, A., & Pop, I. (2014). Flow past a permeable stretching/shrinking sheet in a nanofluid using two-phase model. PLoS One, 9(11).Google Scholar
  12. 12.
    Mamatha, S. U., Raju, C. S. K., Madhavi, G., & Mahesha. (2017). Unsteady 3D MHD Carreau and Casson fluids over a stretching sheet with non-uniform heat source/sink. Chemical Process and Engineering Research, 52, 10–23.Google Scholar
  13. 13.
    Santhosh, H. B., Mahesha, & Raju, C. S. K. (2018). Partial slip flow of radiated Carreau dusty nanofluid over exponentially stretching sheet with non-uniform heat source or sink. Journal of Nanofluid, 7(1), 72–81.CrossRefGoogle Scholar
  14. 14.
    Mamatha, S. U., Mahesha, & Raj, C. S. K. (2017). Multiple slips on magnetohydrodynamic Carreau dusty nano fluid over a stretched surface with Cattaneo-Christov heat flux. Journal of Nanofluids, 6(6), 1074–1081.CrossRefGoogle Scholar
  15. 15.
    Babu, N., Neeraja, G., Raju, C. S. K., & Cattaneo-Christov. (2017). Heat flux on Blasius and Sakiadis flow in a suspension of carbon nanotubes with thermal radiation. Journal of Nanofluids, 6(6), 1166–1172.CrossRefGoogle Scholar
  16. 16.
    Seth, G. S., Sharma, R., & Kumbhakar, B. (2016). Heat and mass transfer effects on unsteady MHD natural convection flow of a chemically reactive and radiating fluid through a porous medium past a moving vertical plate with arbitrary ramped temperature. Journal of Fluid Mechanics, 9(1), 103–117.CrossRefGoogle Scholar
  17. 17.
    Seth, G. S., Tripathi, R., Sharma, R., & Chamkha, A. J. (2017). MHD double diffusive natural convection flow over exponentially accelerated inclined plate, Journal of Mechanics. Journal of Mechanics, 33(1), 87–99.CrossRefGoogle Scholar
  18. 18.
    Raju, C. S. K., & Sandeep, N. (2016). Unsteady three-dimensional flow of Casson-Carreau fluids past a stretching surface. Alexandria Engineering Journal, 55, 1115–1126.CrossRefGoogle Scholar
  19. 19.
    Raju, C. S. K., & Sandeep, N. (2017). Unsteady Casson nanofluid flow over a rotating cone in a rotating frame filled with ferrous nanoparticles: a numerical study. Journal of Magnetism and Magnetic Materials, 421, 216–224.CrossRefGoogle Scholar
  20. 20.
    Raju, C. S. K., Sekhar, K. R., Ibrahim, S. M., Lorenzini, G., Viswanatha Reddy, G., & Lorenzini, E. (2017). Variable viscosity on unsteady dissipative Carreau fluid over a truncated cone filled with titanium alloy nanoparticles. Continuum Mechanics and Thermodynamics.
  21. 21.
    Raju, C. S. K., Hoque, M. M., Anika, N. N., Mamatha, S. U., & Sharma, P. (2017). Natural convective heat transfer analysis of MHD unsteady Carreau nanofluid over a cone packed with alloy nanoparticles. Powder Technology, 317, 408–416.CrossRefGoogle Scholar
  22. 22.
    Krishnamurthy, M. R., Gireesha, B. J., Gorla, R. S. R., & Prasannakumara, B. C. (2016). Suspended particle effect on slip flow and melting heat transfer of nanofluid over a stretching sheet embedded in a porous medium in the presence of nonlinear thermal radiation. Journal of Nanofluids, 5, 502–510.CrossRefGoogle Scholar
  23. 23.
    Gireesha, B. J., Mahesha, Ramesha, G. K., & Bagewadi, C. S. (2011). Unsteady flow of a dusty fluid through a channel having triangular cross-section in Frenet frame field system. Acta Universitatis Apulensis, (23), 53–75.Google Scholar
  24. 24.
    Nandkeolyar, R., Seth, G. S., Makinde, O. D., Sibanda, P., & Ansari, M. S. (2013). Unsteady hydromagnetic natural convection flow of a dusty fluid past an impulsively moving vertical plate with ramped temperature in the presence of thermal radiation. ASME Journal of Applied Mechanics, 80(1–-9), 061003.CrossRefGoogle Scholar
  25. 25.
    Rosali, H., & Ishak, A. (2014). Stagnation-point flow over a stretching/shrinking sheet in a porous medium. American Institute of Physics, 1571, 949–955.Google Scholar
  26. 26.
    Pal, D., Mandal, G., & Vajravalu, K. (2015). Mixed convection stagnation-point flow of nanofluids over a stretching/shrinking sheet in a porous medium with internal heat generation/absorption. Communication in Numerical Analysis, 1, 30–50.MathSciNetCrossRefGoogle Scholar
  27. 27.
    Mamatha, S. U., Krishna Murthy, M., Raju, C. S. K., & Hoque, M. M. Heat transfer effects on MHD flow of jeffrey fluid over a shrinking sheet with heat source/sink and mass suction. International Journal of Research in Science & Engineering ISSN: 2394-8280.Google Scholar
  28. 28.
    Murthy, M. K., Raju, C. S. K., Hoque, M. M., & Anika, N. N. (2017). Magnetohydrodynamic Jeffrey fluid over a porous unsteady shrinking sheet with suction parameter: numerical approach. International Journal of Advanced Thermofluid Research, 3(1) ISSN 2455-1368.Google Scholar
  29. 29.
    Mahesha, Santhosh, H. B., & Raju, C. S. K. (2018). Unsteady Carreau two-phase flow in deformation of graphene nano particles with heat generation and connective conditions. Journal of Nanofluids, 7, 1–8.CrossRefGoogle Scholar
  30. 30.
    Upadhya, S., Mamatha, C. S., Raju, K., Saleem, S., & Alderremy, A. A. (2018). Modified Fourier heat flux on MHD flow over stretched cylinder filled with dust, graphene and silver nanoparticles. Results in Physics, 9, 1377–1385.CrossRefGoogle Scholar
  31. 31.
    Mamatha, S. U., Mahesha, & Raju, C. S. K. (2018). Unsteady flow of Carraeu fluid in a suspension of dust and graphene nano particles with Cattaneuo- Christov heat flux. Journal of Heat Transfer, 140, 092401.CrossRefGoogle Scholar
  32. 32.
    Malik, M. Y., Zehra, I., & Nadeem, S. (2014). Flows of Carreau fluid with pressure dependent viscosity in a variable porous medium: application of polymer melt. Alexandria Engineering Journal, 53(2), 427–435.CrossRefGoogle Scholar
  33. 33.
    Sibanda, P., & Makinde, O. D. (2010). On steady MHD flow and heat transfer due to a rotating disk in a porous medium with Ohmic heating and viscous dissipation. International Journal of Numerical Methods for Heat and Fluid Flow, 20(3), 269–285.CrossRefGoogle Scholar
  34. 34.
    Mebarek-Oudina, F. (2014). Numerical modeling of MHD stability in a cylindrical configuration. Journal of the Franklin Institute, 351(2), 667–681.MathSciNetCrossRefzbMATHGoogle Scholar
  35. 35.
    Hayat, T., Farooq, M., Alsaedi, A., & Al-Solamy, F. (2015) Impact of Cattaneo-Christov heat flux in the flow over a stretching sheet with variable thickness. Aip Advances 5(8): 087159Google Scholar
  36. 36.
    Makinde, O. D., & Chinyoka, T. (2010). Numerical investigation of transient heat transfer to hydromagnetic channel flow with radiative heat and convective cooling. Communications in Nonlinear Science and Numerical Simulation, 15, 3919–3930.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • H. B. Santhosh
    • 1
  • Mahesha
    • 2
  • S. Suresh Kumar Raju
    • 3
    Email author
  • C. S. K. Raju
    • 1
  1. 1.Department of Mathematics School of TechnologyGITAM Deemed To Be UniversityBengaluruIndia
  2. 2.Department of MathematicsUniversity B.D.T. College of EngineeringDavangereIndia
  3. 3.Department of Mathematics and Statistics, College of ScienceKing Faisal UniversityHofufSaudi Arabia

Personalised recommendations