Skip to main content
Log in

Mixed Convective Flow of Sisko Nanofluids Over a Curved Surface with Entropy Generation and Joule Heating

  • Research Article-Mechanical Engineering
  • Published:
Arabian Journal for Science and Engineering Aims and scope Submit manuscript

Abstract

This article addresses the problem of entropy generation optimization of Sisko nanofluid over a curved stretching sheet under the combined effects of mixed convection, Joule heating, and Lorentz force. The Brownian motion (Nb) and thermophoretic diffusion (Nt) effects are also studied. The mass and heat transportation are formulated by convective conditions, Joule heating effects and Lorentz forces. The mathematical formulation of this problem results in a system of nonlinear PDE’s and along with the curvilinear coordinate system. These partial differential equations are transformed into ordinary differential equations by utilizing suitable geometry based similarity transformations. The resulting ordinary differential equations are solved numerically by using BVP4C. The effects of all physical parameters on the velocity, temperature, and concentration are discussed for different values of the involved parameters through graphs. It can be seen that an increase in the values of magnetic parameters leads to the decline of the velocity field. The temperature and concentration profile increase with the increase in Biot number. The irreversibility rate and Bejan number showed declining behavior for increasing values of the Brinkman number. Additionally, the local skin-friction coefficient, local Nusselt and Sherwood numbers are tabulated to discuss the physical phenomenon. The novelty of this work is that the Sisko fluid flow through curved surface along with above mentioned effects is studied first time. This study is extremely beneficial in continuous casting, drawing of annealing wires, paper product, glass fiber, and polymer sheet extrusion from dye and many other real-world processes that involve stretching velocities.

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

Access this article

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

Instant access to the full article PDF.

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
Fig. 26
Fig. 27

Similar content being viewed by others

References

  1. Sisko, A.W.: The flow of lubricating greases. Ind. Eng. Chem. 50, 1789–1792 (1958). https://doi.org/10.1021/ie50588a042

    Article  Google Scholar 

  2. Andersson, H.I.; Bech, K.H.; Dandapat, B.S.: Magnetohydrodynamic flow of a power-law fluid over a stretching sheet. Int. J. Non Linear Mech. 27, 929–936 (1992). https://doi.org/10.1016/j.ijnonlinmec.2006.12.006

    Article  MATH  Google Scholar 

  3. Denier, J.P.; Dabrowski, P.P.: On the boundary-layer equations for power-law fluids. In: Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences. 460, pp. 3143-3158 (2004)

  4. Cortell, R.: A note on magnetohydrodynamic flow of a power-law fluid over a stretching sheet. Appl. Math. Comput. 168, 557–566 (2005)

    MathSciNet  MATH  Google Scholar 

  5. Abbas, T.; Ahmad, B.; Khan, S.U.; Haq, E.U.; Hassan, Q.M.; Wakif, A.: Couple stress flow of exponentially stretching sheet with Cattaneo–Christov heat flux model. Heat Transf. 51, 4819–4832 (2022)

    Article  Google Scholar 

  6. Mambili-Mamboundou, H.; Khan, M.; Hayat, T.; Mahomed, F.: Reduction and solutions for magnetohydrodynamic flow of a Sisko fluid in a porous medium. J. Porous Media 12, 695–714 (2009)

    Article  Google Scholar 

  7. Khan, M.; Munawar, S.; Abbasbandy, S.: Steady flow and heat transfer of a Sisko fluid in annular pipe. Int. J. Heat Mass Transf. 53, 1290–1297 (2010)

    Article  MATH  Google Scholar 

  8. Choi, S.U.S.: Enhancing thermal conductivity of fluids with nanoparticles. Proc. ASME Int. Mech. Eng. Cong. Exp. 66, 99–105 (1995)

    Google Scholar 

  9. Riaz, A.; Hassan, Q.M.; Abbas, T.; Ghachem, K.; Majeed, A.; Noori, F.M.; Kolsi, L.: A study on effectiveness of the variational theory in fluid dynamics applications. Alex. Eng. J. 61, 10779–10789 (2022)

    Article  Google Scholar 

  10. Khan, J.A.; Mustafa, M.; Hayat, T.; Turkyilmazoglu, M.; Alsaedi, A.: Numerical study of nanofluid flow and heat transfer over a rotating disk using Buongiorno’s model. Int. J. Numer. Methods Heat Fluid Flow. 27, 221–234 (2017)

  11. Ahmad, L.; Khan, M.: Numerical simulation for MHD flow of Sisko nanofluid over a moving curved surface: a revised model. Microsyst. Technol. 25, 2411–2428 (2018)

    Article  Google Scholar 

  12. Ali, R., Shahzad, A., us Saher, K., Elahi, Z., Abbas, T.: The thin film flow of al2o3 nanofluid particle over an unsteady stretching surface. Case Stud. Therm. Eng. 29, 101695 (2022)

  13. Khan, U.; Ahmed, N.; Khan, S.I.; Mohyud-din, S.T.: Thermo-diffusion effects on MHD stagnation point flow towards a stretching sheet in a nanofluid. Propuls. Power Res. 3, 151–158 (2014)

    Article  Google Scholar 

  14. Mustafa, M.; Hayat, T.; Pop, I.; Asghar, S.; Obaidat, S.: Stagnation-point flow of a nanofluid towards a stretching sheet. Int. J. Heat Mass Transf. 54, 5588–5594 (2011)

    Article  MATH  Google Scholar 

  15. Haq, E.U.; Khan, S.U.; Abbas, T.; Smida, K.; Hassan, Q.M.; Ahmad, B.; Khan, M.I.; Guedri, K.; Kumam, P.; Galal, A.M.: Numerical aspects of thermo migrated radiative nanofluid flow towards a moving wedge with combined magnetic force and porous medium. Sci. Rep. 12 (2022)

  16. Ali, M.; Khan, W.A.; Sultan, F.; Shahzad, M.: Numerical investigation on thermally radiative time-dependent Sisko nanofluid flow for curved surface. Physica A Stat. Mech. Appl. 550, 124012 (2020)

  17. Sharma, R.; Bisht, A.: MHD flow of Sisko nanofluid over a stretching sheet with Joule Heating. In: Proceedings of the International Research Conference - 12TH EURECA 2019 (2019)

  18. Hussain, A.; Malik, M.Y.; Salahuddin, T.; Bilal, S.; Awais, M.: Combined effects of viscous dissipation and joule heating on MHD Sisko nanofluid over a stretching cylinder. J. Mol. Liq. 231, 341–352 (2017)

    Article  Google Scholar 

  19. Ahmad, L.; Munir, A.; Khan, M.: Locally non-similar and thermally radiative Sisko fluid flow with magnetic and joule heating effects. J. Magn. Magn. Mater. 487, 165284 (2019)

  20. El-dabe, N.T.M.; Mostapha, D.R.: Hall current and Joule heating effects on peristaltic flow of a Sisko fluid with mild stenosis through a porous medium in a tapered artery with slip and convective boundary conditions. Sains Malaysiana. 49, 1175–1190 (2020)

    Article  Google Scholar 

  21. Li, Z.; Shafee, A.; Kandasamy, R.; Ramzan, M.; Al-Mdallal, Q.M.: Nanoparticle transportation through a permeable duct with Joule Heating Influence. Microsyst. Technol. 25, 3571–3580 (2018)

    Article  Google Scholar 

  22. Nadeem, S.; Ahmad, S.; Muhammad, N.: Cattaneo–Christov flux in the flow of a viscoelastic fluid in the presence of newtonian heating. J. Mol. Liq. 237, 180–184 (2017)

    Article  Google Scholar 

  23. Abbas, T.; Majeed, A.; Ahmad, B.; Noveel Sadiq, M.; Ul Hassan, Q.M.; Ullah, H.; Al-Mekhlafi, S.M.: Dual solution with heat transfer through moving porous plate of an unsteady incompressible viscous fluid. J. Chem. 2022, 1–12 (2022)

    Article  Google Scholar 

  24. Hayat, T.; Aslam, N.; Alsaedi, A.; Rafiq, M.: Numerical study for MHD peristaltic transport of Sisko nanofluid in a curved channel. Int. J. Heat Mass Transf. 109, 1281–1288 (2017)

    Article  Google Scholar 

  25. Awais, M.; Malik, M.Y.; Bilal, S.; Salahuddin, T.; Hussain, A.: Magnetohydrodynamic (MHD) flow of Sisko fluid near the axisymmetric stagnation point towards a stretching cylinder. Results Phys. 7, 49–56 (2017)

    Article  Google Scholar 

  26. Madhu, M.; Reddy, C.S.; Kishan, N.: Magnetohydrodynamic flow and heat transfer to Sisko nanofluid over a wedge. Int. J. Fluid Mech. Res. 44, 1–13 (2017)

    Article  Google Scholar 

  27. Hayat, T., Ullah, I., Alsaedi, A., Asghar, S.: Magnetohydrodynamics stagnation-point flow of Sisko Liquid with melting heat transfer and heat generation/absorption. J. Therm. Sci. Eng. Appl. 10 (2018)

  28. Prasannakumara, B.C.; Gireesha, B.J.; Krishnamurthy, M.R.; Ganesh Kumar, K.: MHD flow and nonlinear radiative heat transfer of Sisko nanofluid over a nonlinear stretching sheet. Inf. Med. Unlocked. 9, 123–132 (2017)

    Article  Google Scholar 

  29. Khan, A.S.; Nie, Y.; Shah, Z.: Impact of thermal radiation on magnetohydrodynamic unsteady thin film flow of Sisko fluid over a stretching surface. Processes. 7, 369 (2019)

  30. Khan, U.; Zaib, A.; Ishak, A.: Magnetic field effect on Sisko fluid flow containing gold nanoparticles through a porous curved surface in the presence of radiation and partial slip. Mathematics. 9, 921 (2021)

  31. Muhammad, N.; Nadeem, S.; Haq, R.U.: Heat transport phenomenon in the ferromagnetic fluid over a stretching sheet with thermal stratification. Results Phys. 7, 854–861 (2017)

    Article  Google Scholar 

  32. Pal, D.; Mandal, G.: Magnetohydrodynamic heat and mass transfer of Sisko nanofluid past a stretching sheet with nonlinear thermal radiation and convective boundary condition. J. Nanofluids 8, 852–860 (2019)

    Article  Google Scholar 

  33. Tanveer, A.; Hayat, T.; Alsaedi, A.; Ahmad, B.: Mixed convective peristaltic flow of Sisko fluid in curved channel with homogeneous-heterogeneous reaction effects. J. Mol. Liq. 233, 131–138 (2017)

    Article  Google Scholar 

  34. Ahmad, B., Nawaz, A., Smida, K., Khan, S.U., Khan, M.I., Abbas, T., Reddy, Y.D., Guedri, K., Malik, M.Y., Goud, B.S., Galal, A.M.: Thermal diffusion of Maxwell nanoparticles with diverse flow features: Lie group simulations. Int. Commun. Heat Mass Transf. 136, 106164 (2022)

  35. Muhammad, R.; Khan, M.I.; Jameel, M.; Khan, N.B.: Fully developed Darcy–Forchheimer mixed convective flow over a curved surface with activation energy and entropy generation. Comput. Methods Programs Biomed. 188, 105298 (2020)

  36. Khan, A.S.; Nie, Y.; Shah, Z.: Impact of thermal radiation on magnetohydrodynamic unsteady thin film flow of Sisko fluid over a stretching surface. Processes. 7, 369 (2019)

  37. Farooq, S.; Hayat, T.; Alsaedi, A.; Ahmad, B.: Numerically framing the features of second order velocity slip in mixed convective flow of Sisko nanomaterial considering gyrotactic microorganisms. Int. J. Heat Mass Transf. 112, 521–532 (2017)

    Article  Google Scholar 

  38. Abbas, T.; Ahmad, B.; Majeed, A.; Muhammad, T.; Ismail, M.: Numerical investigations of radiative flow of viscous fluid through porous medium. J. Magn. 26, 277–284 (2021)

    Article  Google Scholar 

  39. Bejan, A.: A study of entropy generation in fundamental convective heat transfer. J. Heat Transf. 101, 718–725 (1979)

    Article  Google Scholar 

  40. Shit, G.C.; Haldar, R.; Mandal, S.: Entropy generation on MHD flow and convective heat transfer in a porous medium of exponentially stretching surface saturated by nanofluids. Adv. Powder Technol. 28, 1519–1530 (2017)

    Article  Google Scholar 

  41. Hayat, T., Masood, F., Qayyum, S., Alsaedi, A.: Entropy generation minimisation: nonlinear mixed convective flow of Sisko nanofluid. Pramana 93 (2019)

  42. Hayat, T., Qayyum, S., Alsaedi, A., Ahmad, B.: Entropy generation minimization: Darcy–Forchheimer nanofluid flow due to curved stretching sheet with partial slip. Int. Commun. Heat Mass Transf. 111, 104445 (2020)

  43. Hayat, T.; Khan, M.I.; Qayyum, S.; Khan, M.I.; Alsaedi, A.: Entropy generation for flow of Sisko fluid due to rotating disk. J. Mol. Liq. 264, 375–385 (2018)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Muhammad Bilal Ashraf.

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

Tanveer, A., Ashraf, M.B. Mixed Convective Flow of Sisko Nanofluids Over a Curved Surface with Entropy Generation and Joule Heating. Arab J Sci Eng 48, 11263–11275 (2023). https://doi.org/10.1007/s13369-022-07413-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13369-022-07413-0

Keywords

Navigation