Skip to main content
SpringerLink
Log in

Variable viscosity effects on dynamic of non-Newtonian fluid nanofluid over a paraboloid of revolution via Keller box method

  • Regular Article
  • Published:
The European Physical Journal Plus Aims and scope Submit manuscript

Abstract

The variable viscosity effects on MHD flow of Boger nanofluid due to paraboloid of revolution with chemical reactive species is investigated. It is assumed that the base fluid has a uniform suspension of nanoparticles, and Reynolds exponential viscosity model has been employed. Intensification in thermal transport of base fluids has drawn our attention to increasing thermal conductivity. Similarity transformation is active to reach the partial differential equations into ordinary differential form but boundary layer approximation is utilized for the governing equations. For numerical suction, we considered Keller box method as tool for numerical simulation to obtain the flow field of velocity, heat and volume friction profile. The leading factors of model are varied in their appropriate limits, to visualize their part as graphically. It has been observed that Boger fluid becomes extremely flexible at constant values of viscosity due to which the velocity profile \(f^{\prime } (\zeta )\) is directly increased with large values of the solvent fraction parameter \(\beta_{2}\) while ratio of relaxation time parameter \(\beta_{1}\) indicates the tendency to be decreased the velocity profile. It is observed that the fluid velocity for variable viscosity is slower but it is higher at constant values of \(\lambda\), and an opposite trend is reported in temperature profile. The skin friction \(- f^{\prime \prime } (0)\) is boosted but opposite trend is observed in local Nusselt \(- \theta^{\prime } (0)\) and local Sherwood numbers \(- \phi^{\prime } (0)\) with the increasing values of magnetic parameter.

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
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25

Similar content being viewed by others

Data Availability Statement

The numerical data used to support the findings of this study are included within the article.

References

  1. J. Buongiorno, L.W. Hu, S.J. Kim, R. Hannink, B.A. Truong, E. Forrest, Nanofluids for enhanced economics and safety of nuclear reactors: an evaluation of the potential features, issues, and research gaps. Nucl. Technol. 162, 80–91 (2008)

    Article  ADS  Google Scholar 

  2. S.U. Choi, J.A. Eastman, Enhancing thermal conductivity of fluids with nanoparticles. Argonne National Lab., IL (United States) (1995)

  3. S. Nadeem, S. Akram, Influence of inclined magnetic field on peristaltic flow of a Williamson fluid model in an inclined symmetric or asymmetric channel. Math. Comput. Model. 152, 107–119 (2010)

    Article  MathSciNet  Google Scholar 

  4. Y. Wei, S.U. Rehman, N. Fatima, B. Ali, L. Ali, J.D. Chung, N.A. Shah, Significance of dust particles, nanoparticles radius, Coriolis and Lorentz forces: the case of Maxwell dusty fluid. Nanomaterials 12(9), 1512 (2022)

    Article  Google Scholar 

  5. R.S. Gorla, B.J. Gireesha, Dual solutions for stagnation-point flow and convective heat transfer of a Williamson nanofluid past a stretching/shrinking sheet. Heat Mass Transf. 152, 1153–1162 (2016)

    Article  ADS  Google Scholar 

  6. H. Li, S. Liu, Z. Dai, J. Bao, X. Yang, Applications of nanomaterials in electrochemical enzyme biosensors. Sensors. 9, 8547–8561 (2009)

    Article  ADS  Google Scholar 

  7. A.U. Yahya, N. Salamat, D. Habib, B. Ali, S. Hussain, S. Abdal, Implication of Bio-convection and Cattaneo–Christov heat flux on Williamson Sutterby nanofluid transportation caused by a stretching surface with convective boundary. Chin. J. Phys. 73, 706–718 (2021)

    Article  MathSciNet  Google Scholar 

  8. D. Habib, S. Abdal, R. Ali, D. Baleanu, I. Siddique, On bioconvection and mass transpiration of micropolar nanofluid dynamics due to an extending surface in existence of thermal radiations. Case Stud. Therm. Eng. 27, 10123 (2021)

    Article  Google Scholar 

  9. S.U. Rehman, N. Fatima, B. Ali, M. Imran, L. Ali, N.A. Shah, J.D. Chung, The Casson dusty nanofluid: significance of darcy-forchheimer law, magnetic field, and non-Fourier heat flux model subject to stretch surface. Mathematics. 10(16), 2877 (2022)

    Article  Google Scholar 

  10. Q. Raza, M.Z.A. Qureshi, B.A. Khan, A. Kadhim Hussein, B. Ali, N.A. Shah, J.D. Chung, Insight into dynamic of mono and hybrid nanofluids subject to binary chemical reaction, activation energy, and magnetic field through the porous surfaces. Mathematics. 10(16), 3013 (2022)

    Article  Google Scholar 

  11. M.Z.A. Qureshi, M. Faisal, Q. Raza, B. Ali, T. Botmart, N.A. Shah, Morphological nanolayer impact on hybrid nanofluids flow due to dispersion of polymer/CNT matrix nanocomposite material. AIMS Math. 8(1), 633–656 (2023). https://doi.org/10.3934/math.2023030

    Article  MathSciNet  Google Scholar 

  12. B. Ali, S. Hussain, M. Shafique, D. Habib, G. Rasool, Analyzing the interaction of hybrid base liquid C2H6O2-H2O with hybrid nano-material Ag-MoS2 for unsteady rotational flow referred to an elongated surface using modified Buongiorno’s model: FEM simulation. Math. Comput. SimulComput. Simul. 190, 57–74 (2021)

    Article  Google Scholar 

  13. D. Habib, N. Salamat, S. Abdal, I. Siddique, M. Salimi, A. Ahmadian, On time dependent MHD nanofluid dynamics due to enlarging sheet with bioconvection and two thermal boundary conditions. Microfluid. Nanofluid. 26(2), 1–15 (2022)

    Article  Google Scholar 

  14. D. Habib, N. Salamat, S. Abdal, I. Siddique, M.C. Ang, A. Ahmadian, On the role of bioconvection and activation energy for time dependent nanofluid slip transpiration due to extending domain in the presence of electric and magnetic fields. Ain Shams Eng. J. 13, 101519 (2021)

    Article  Google Scholar 

  15. A.U. Yahya, N. Salamat, W.H. Huang, I. Siddique, S. Abdal, S. Hussain, Thermal charactristics for the flow of Williamson hybrid nanofluid (MoS2+ ZnO) based with engine oil over a streched sheet. Case Stud. Therm. Eng. 26, 101196 (2021)

    Article  Google Scholar 

  16. S. Abdal, S. Hussain, I. Siddique, A. Ahmadian, M. Ferrara, On solution existence of MHD Casson nanofluid transportation across an extending cylinder through porous media and evaluation of priori bounds. Sci. Rep. 11(1), 1–16 (2021)

    Article  Google Scholar 

  17. T. Javed, M. Faisal, I. Ahmad, Actions of viscous dissipation and Ohmic heating on bidirectional flow of a magneto-Prandtl nanofluid with prescribed heat and mass fluxes. Heat Transf. 49(8), 4801–4819 (2020)

    Article  Google Scholar 

  18. I. Khan, A. Hussain, M.Y. Malik, S. Mukhtar, On magnetohydrodynamics Prandtl fluid flow in the presence of stratification and heat generation. Physica A 540, 123008 (2020)

    Article  MathSciNet  Google Scholar 

  19. T. Hayat, F. Shah, A. Alsaedi, B. Ahmad, Entropy optimized dissipative flow of effective Prandtl number with melting heat transport and Joule heating. Int. Commun. Heat Mass Transf. 111, 104454 (2020)

    Article  Google Scholar 

  20. C.H. Amanulla, S. Saleem, A. Wakif, M.M. Al Qarni, MHD Prandtl fluid flow past an isothermal permeable sphere with slip effects. Case Stud. Therm. Eng. 14, 100447 (2019)

    Article  Google Scholar 

  21. M. Awais, S. Bilal, K. Ur Rehman, M.Y. Malik, Numerical investigation of MHD Prandtl melted fluid flow towards a cylindrical surface: comprehensive outcomes. Can. J. Phys. 98(3), 223–232 (2020)

    Article  ADS  Google Scholar 

  22. N.T. Eldabe, G.M. Moatimid, A.A. ElShekhipy, N.F. Aballah, Mixed convective peristaltic flow of Eyring–Prandtl fluid with chemical reaction and variable electrical conductivity in a tapered asymmetric channel. Heat Transf. Asian Res. 48(5), 1946–1962 (2019)

    Article  Google Scholar 

  23. M. Faiz, D. Habib, I. Siddique, J. Awrejcewicz, W. Pawłowski, S. Abdal, N. Salamat, Multiple slip effects on time dependent axisymmetric flow of magnetized Carreau nanofluid and motile microorganisms. Sci. Rep. 12(1), 14259 (2022)

    Article  ADS  Google Scholar 

  24. B. Ali, S. Hussain, M. Shafique, D. Habib, G. Rasool, Analyzing the interaction of hybrid base liquid C2H6O2–H2O with hybrid nano-material Ag–MoS2 for unsteady rotational flow referred to an elongated surface using modified Buongiorno’s model: FEM simulation. Math. Comput. Simul 190, 57–74 (2021)

    Article  Google Scholar 

  25. M.M. Alanazi, A. Ahmed Hendi, N.A. Ahammad, B. Ali, S. Majeed, N.A. Shah, Significance of ternary hybrid nanoparticles on the dynamics of nanofluids over a stretched surface subject to gravity modulation. Mathematics. 11(4), 809 (2023)

    Article  Google Scholar 

  26. T. Salahuddin, M. Awais, W.F. Xia, Variable thermo-physical characteristics of Carreau fluid flow by means of stretchable paraboloid surface with activation energy and heat generation. Case Stud. Therm. Eng. 25, 100971 (2021)

    Article  Google Scholar 

  27. O.A. Abegunrin, S.O. Okhuevbie, I.L. Animasaun, Comparison between the flow of two non-Newtonian fluids over an upper horizontal surface of paraboloid of revolution: boundary layer analysis. Alex. Eng. J. 55(3), 1915–1929 (2016)

    Article  Google Scholar 

  28. T. Salahuddin, M. Awais, Z. Salleh, A flow study of Carreau fluid near the boundary layer region of paraboloid surface with viscous dissipation and variable fluid properties. J. Market. Res. 14, 901–909 (2021)

    Google Scholar 

  29. U. Nazir, N.H. Abu-Hamdeh, M. Nawaz, S.O. Alharbi, W. Khan, Numerical study of thermal and mass enhancement in the flow of Carreau–Yasuda fluid with hybrid nanoparticles. Case Stud. Therm. Eng. 27, 101256 (2021)

    Article  Google Scholar 

  30. M.M. Alanazi, A.A. Hendi, Q. Raza, M.A. Rehman, M.Z.A. Qureshi, B. Ali, N.A. Shah, Numerical computation of hybrid morphologies of nanoparticles on the dynamic of nanofluid: the case of blood-based fluid. Axioms. 12(2), 163 (2023)

    Article  Google Scholar 

  31. M. Khan, T. Salahuddin, M.Y. Malik, M.S. Alqarni, A.M. Alqahtani, Numerical modeling and analysis of bioconvection on MHD flow due to an upper paraboloid surface of revolution. Physica A 553, 124231 (2020)

    Article  MathSciNet  Google Scholar 

  32. M. Khan, A. Shahid, T. Salahuddin, M.Y. Malik, M. Mushtaq, Heat and mass diffusions for Casson nanofluid flow over a stretching surface with variable viscosity and convective boundary conditions. J. Braz. Soc. Mech. Sci. Eng. 40, 1–10 (2018)

    Article  Google Scholar 

  33. L. Ali, X. Liu, B. Ali, S. Abdal, R.M. Zulqarnain, Finite element analysis of unsteady MHD Blasius and Sakiadis flow with radiation and thermal convection using Cattaneo–Christov heat flux model. Phys. Scr. 96(12), 125219 (2021)

    Article  ADS  Google Scholar 

  34. S.A. Khan, B. Ali, C. Eze, K.T. Lau, L. Ali, J. Chen, J. Zhao, Magnetic dipole and thermal radiation impact on stagnation point flow of micropolar based nanofluids over a vertically stretching sheet: finite element approach. Processes 9(7), 1089 (2021)

    Article  Google Scholar 

  35. H.B. Keller, A new difference scheme for parabolic problems. In Numerical Solution of Partial Differential Equations–II, pp. 327–350. Academic Press (1971)

  36. T. Cebeci, P. Bradshaw, Physical and Computational Aspects of Convective Heat Transfer. Springer (2012)

  37. D. Habib, N. Salamat, S. Hussain, S. Abdal, B. Ali, Insight of Riga effects on dynamic of Prandtl nanofluid over a moving wedge via Keller box approach. Waves Random Complex Media 1–30 (2022)

  38. N. Salamat, S. Hussain, B. Ali, S. Abdal, Significance of Stephen blowing and Lorentz force on dynamics of Prandtl nanofluid via Keller box approach. Int. Commun. Heat Mass Transf. 128, 105599 (2021)

    Article  Google Scholar 

  39. D. Habib, N. Salamat, S.H.S. Abdal, B. Ali, Numerical investigation for MHD Prandtl nanofluid transportation due to a moving wedge: Keller box approach. Int. Commun. Heat Mass Transf. 135, 106141 (2022)

    Article  Google Scholar 

  40. J. Zhu, D. Yang, L. Zheng, X. Zhang, Effects of second order velocity slip and nanoparticles migration on flow of Buongiorno nanofluid. Appl. Math. Lett. 52, 183–191 (2016)

    Article  MathSciNet  Google Scholar 

  41. S. Abdal, A. Mariam, B. Ali, S. Younas, L. Ali, D. Habib, Implications of bioconvection and activation energy on Reiner-Rivlin nanofluid transportation over a disk in rotation with partial slip. Chin. J. Phys. 73, 672–683 (2021)

    Article  MathSciNet  Google Scholar 

  42. B. Ali, I. Siddique, A. Shafiq, S. Abdal, I. Khan, A. Khan, Magnetohydrodynamic mass and heat transport over a stretching sheet in a rotating nanofluid with binary chemical reaction, non-fourier heat flux, and swimming microorganisms. Case Stud. Therm. Eng. 28, 101367 (2021)

    Article  Google Scholar 

  43. S.U. Rehman, N. Fatima, B. Ali, M. Imran, L. Ali, N.A. Shah, J.D. Chung, The Casson dusty nanofluid: significance of Darcy–Forchheimer law, magnetic field, and non-Fourier heat flux model subject to stretch surface. Mathematics 10(16), 2877 (2022)

    Article  Google Scholar 

  44. S.A.A. Shah, N.A. Ahammad, B. Ali, K. Guedri, A.U. Awan, F. Gamaoun, Tag-ElD in, E. M., Significance of bio-convection, MHD, thermal radiation and activation energy across Prandtl nanofluid flow: a case of stretching cylinder. Int. Commun. Heat Mass Transf. 137, 106299 (2022)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Khwaja Fareed University of Engineering and Information Technology, Rahim Yar Khan, Pakistan

    Danial Habib, Nadeem Salamat & Sohaib Abdal

  2. Department of Mathematics, Government College University Faisalabad, Layyah Campus, Faisalabad, Pakistan

    Danial Habib

  3. School of Aerospace and Mechanical Engineering, Nanyang Technological University, Singapore, Singapore

    Sajjad Hussain

  4. School of Mathematics, Northwest University, No. 229 North Taibai Avenue, Xi’an, 710049, China

    Sohaib Abdal

  5. Mechanical Engineering Department, College of Engineering, University of Babylon, Hilla, 00964, Iraq

    Ahmed Kadhim Hussein

  6. School of Mechanical Engineering and Automation, Harbin Institute of Technology, Shenzhen, 518055, China

    Bagh Ali

Authors
  1. Danial Habib
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nadeem Salamat
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sajjad Hussain
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Sohaib Abdal
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Ahmed Kadhim Hussein
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Bagh Ali
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bagh Ali.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Habib, D., Salamat, N., Hussain, S. et al. Variable viscosity effects on dynamic of non-Newtonian fluid nanofluid over a paraboloid of revolution via Keller box method. Eur. Phys. J. Plus 139, 427 (2024). https://doi.org/10.1140/epjp/s13360-024-05242-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/s13360-024-05242-8

Search

Navigation