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A theoretical investigation of the MHD water-based hybrid nanofluid flow over a convectively heated rotating disk surface with velocity slips and zero mass flux conditions

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Abstract

In the present model, we have studied the water-based hybrid nanofluid flow through a revolving disk. The slip and convective constraints at boundary are carried out in the problem. In the model, aluminum Al2O3 and copper Cu nanoparticles are taken into consideration to form a hybrid nanofluid with base fluid water. An appropriate set of similarity variables are taken into consideration to transform the PDEs into ODEs. The solution to the model has been gained by taking the HAM procedure. The convergence solution of the model is presented in the Figures’ form. The role of distinct factors in velocities, thermal, and mass concentration sketches are delineated via Figures and Tables. The consequences reveal that the flow profile decelerate with magnetic factor. The skin friction and Nusselt number mounted with mounting in volume fraction. The thermal and concentration distribution rises with escalating thermophoresis factor. An increasing behavior is detected in the temperature distribution with mounting in the heat source factor. The result shows that the variation in hybrid nanofluid is more than nanofluid.

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Data Availability Statement

This manuscript has associated data in a data repository. [Authors’ comment: All data used in this manuscript have been presented within the article.]

Abbreviations

\(a\) :

Angular velocity (m s−1)

\(u_{1} ,u_{2} ,u_{3}\) :

Velocity components (m s−1)

\(C_{p}\) :

Specific heat (J K−1 kg−3)

\(B_{0}\) :

Strength of magnetic field (kg s−1 A−1)

\(C_{\infty }\) :

Ambient concentration (mol m−3)

\(T_{f}\) :

Reference temperature (K)

\(C_{{{\text{fr}}}}\) :

Skin friction (−)

\(N_{{\text{t}}}\) :

Thermophoresis factor (−)

\(N_{{\text{b}}}\) :

Brownian motion factor (−)

\(M\) :

Magnetic parameter (−)

\(D_{{\text{B}}}\) :

Brownian motion coefficient (m2 s−1)

\(E\) :

Activation energy parameter (−)

\(E_{{\text{a}}}\) :

Coefficient of activation energy (J)

\({\text{Sc}}\) :

Schmidt number (−)

\(\Pr\) :

Prandtl number (−)

\({\text{A}}.{\text{E}}\) :

Activation energy (−)

\(k\) :

Thermal conductivity (W k−1 m−1)

\(r,\psi ,z\) :

Coordinates (m)

\(\rho\) :

Density (kg m−3)

\(\beta_{1}\) :

Thermal Biot number (−)

\(\mu\) :

Dynamic viscosity (kg m−1 s−1)

\(\xi\) :

Similarity variable (−)

\(\nu \left( { = \mu /\rho } \right)\) :

Kinematic viscosity (m2 s−1)

\(\omega\) :

Heat source parameter (−)

\(\alpha_{1} ,\;\alpha_{2}\) :

Slip factor (−)

\(\varphi\) :

Volume fraction (−)

\(\sigma\) :

Electrical conductivity (S m−1)

\({\text{hnf}}\) :

Hybrid nanofluid

\({\text{nf}}\) :

Nanofluid

\({\text{f}}\) :

Base-fluid

\({\text{Al}}_{2} {\text{O}}_{3} ,\,{\text{Cu}}\) :

Nanoparticles

References

  1. S.U.S. Choi, Nanofluids: from vision to reality through research, J. Heat Transfer. 131 (2009).

  2. D. Wen, Y. Ding, Formulation of nanofluids for natural convective heat transfer applications. Int. J. Heat Fluid Flow 26, 855–864 (2005)

    Article  Google Scholar 

  3. P. Lin, A. Ghaffari, Steady flow and heat transfer of the power-law fluid between two stretchable rotating disks with non-uniform heat source/sink. J. Therm. Anal. Calorim. 146, 1735–1749 (2021)

    Article  Google Scholar 

  4. H. Waqas, S.U. Khan, I. Tlili, M. Awais, M.S. Shadloo, Significance of bioconvective and thermally dissipation flow of viscoelastic nanoparticles with activation energy features: novel biofuels significance. Symmetry 12, 214 (2020). https://doi.org/10.3390/SYM12020214

    Article  ADS  Google Scholar 

  5. S.K. Rawat, H. Upreti, M. Kumar, Numerical study of activation energy and thermal radiation effects on Oldroyd-B nanofluid flow using the Cattaneo–Christov double diffusion model over a convectively heated stretching sheet. Heat Transf. 50, 5304–5331 (2021). https://doi.org/10.1002/htj.22125

    Article  Google Scholar 

  6. R.J. Punith Gowda, R. Naveen Kumar, A.M. Jyothi, B.C. Prasannakumara, I.E. Sarris, Impact of binary chemical reaction and activation energy on heat and mass transfer of marangoni driven boundary layer flow of a non-Newtonian nanofluid. Processes 9(4), 702 (2021)

    Article  Google Scholar 

  7. N. Bachok, A. Ishak, I. Pop, Stagnation-point flow over a stretching/shrinking sheet in a nanofluid. Nanoscale Res. Lett. 61(6), 1–10 (2011). https://doi.org/10.1186/1556-276X-6-623

    Article  MATH  Google Scholar 

  8. A. Dawar, A. Wakif, T. Thumma, N.A. Shah, Towards a new MHD non-homogeneous convective nanofluid flow model for simulating a rotating inclined thin layer of sodium alginate-based Iron oxide exposed to incident solar energy. Int. Commun. Heat Mass Transf. 130, 105800 (2022)

    Article  Google Scholar 

  9. A. Dawar, A. Wakif, A. Saeed, Z. Shah, T. Muhammad, P. Kumam, Significance of Lorentz forces on Jeffrey nanofluid flows over a convectively heated flat surface featured by multiple velocity slips and dual stretching constraint: a homotopy analysis approach. J. Comput. Des. Eng. 9, 564–582 (2022)

    Google Scholar 

  10. N.S. Khashi’ie, N.C. Roșca, A.V. Roșca, I. Pop, Dual solutions on MHD radiative three-dimensional bidirectional nanofluid flow over a non-linearly permeable shrinking sheet. Alexandria Eng. J. 71, 401–411 (2023)

    Article  Google Scholar 

  11. W. Al-Kouz, W. Owhaib, Numerical analysis of Casson nanofluid three-dimensional flow over a rotating frame exposed to a prescribed heat flux with viscous heating. Sci. Rep. 12, 1–17 (2022)

    Article  Google Scholar 

  12. M.U. Sajid, H.M. Ali, Thermal conductivity of hybrid nanofluids: a critical review. Int. J. Heat Mass Transf. 126, 211–234 (2018)

    Article  Google Scholar 

  13. A. Asadi, M.A. Ibrahim, L. Kok Foong, An experimental study on characterization, stability and dynamic viscosity of CuO–TiO2/water hybrid nanofluid. J. Mol. Liquids 307, 112987 (2020). https://doi.org/10.1016/j.molliq.2020.112987

    Article  Google Scholar 

  14. S. Suresh, K.P. Venkitaraj, M.S. Hameed, J. Sarangan, Turbulent heat transfer and pressure drop characteristics of dilute water based Al2O3–Cu hybrid nanofluids. J. Nanosci. Nanotechnol. 14, 2563–2572 (2014). https://doi.org/10.1166/JNN.2014.8467

    Article  Google Scholar 

  15. N.S. Wahid, N.M. Arifin, Hybrid nanofluid slip flow over an exponentially stretching/shrinking permeable sheet with heat generation. Mathematics 9(1), 30 (2020)

    Article  Google Scholar 

  16. S.U.D. S, S.P.A. Devi, Cu − Al2O3/Water nanofluid flow over a stretching sheet with, (n.d.) 1–26.

  17. 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). https://doi.org/10.3390/MATH10163013

    Article  Google Scholar 

  18. T.H. Alarabi, A.M. Rashad, A. Mahdy, Homogeneous-heterogeneous chemical reactions of radiation hybrid nanofluid flow on a cylinder with joule heating: nanoparticles shape impact. Coatings 11, 1490 (2021)

    Article  Google Scholar 

  19. U. Farooq, M. Tahir, H. Waqas, T. Muhammad, A. Alshehri, M. Imran, Investigation of 3D flow of magnetized hybrid nanofluid with heat source/sink over a stretching sheet. Sci. Rep. 12, 1–15 (2022). https://doi.org/10.1038/s41598-022-15658-w

    Article  Google Scholar 

  20. M. Sajjad, A. Mujtaba, A. Asghar, T.Y. Ying, Dual solutions of magnetohydrodynamics Al2O3 + Cu hybrid nanofluid over a vertical exponentially shrinking sheet by presences of joule heating and thermal slip condition. CFD Lett. 14, 100–115 (2022)

    Article  Google Scholar 

  21. H. Upreti, A. Mishra, The performance evolution of hybrid nanofluid flow over a rotating disk using Cattaneo–Christov double diffusion and Yamada–Ota model, Waves in Random and Complex Media. (2022) 1–21.

  22. M. Sheikholeslami, M. Hatami, D.D. Ganji, Analytical investigation of MHD nanofluid flow in a semi-porous channel. Powder Technol. 246, 327–336 (2013). https://doi.org/10.1016/j.powtec.2013.05.030

    Article  Google Scholar 

  23. Z. Cao, J. Zhao, Z. Wang, F. Liu, L. Zheng, MHD flow and heat transfer of fractional Maxwell viscoelastic nanofluid over a moving plate. J. Mol. Liq. (2016). https://doi.org/10.1016/j.molliq.2016.08.012

    Article  Google Scholar 

  24. A. Alsaedi, M.I. Khan, M. Farooq, N. Gull, T. Hayat, Magnetohydrodynamic ( MHD ) stratified bioconvective flow of nanofluid due to gyrotactic microorganisms. Adv. Powder Technol. (2016). https://doi.org/10.1016/j.apt.2016.10.002

    Article  Google Scholar 

  25. I. Agency, Scientific inquiry and review (SIR), 3 (2019).

  26. A. Dawar, Z. Shah, P. Kumam, W. Khan, S. Islam, Influence of MHD on thermal behavior of darcy-forchheimer nanofluid thin film flow over a nonlinear stretching disc. Coatings 9(7), 446 (2019). https://doi.org/10.3390/coatings9070446

    Article  Google Scholar 

  27. H. Waqas, U. Farooq, R. Naseem, S. Hussain, Case Studies in Thermal Engineering Impact of MHD radiative flow of hybrid nanofluid over a rotating disk. Case Stud. Therm. Eng. 26, 101015 (2021). https://doi.org/10.1016/j.csite.2021.101015

    Article  Google Scholar 

  28. E.A. Algehyne, N.H. Altaweel, A. Saeed, A. Dawar, M. Ramzan, P. Kumam, A semi-analytical passive strategy to examine the water-ethylene glycol (50: 50)-based hybrid nanofluid flow over a spinning disk with homogeneous–heterogeneous reactions. Sci. Rep. 12(1), 17105 (2022). https://doi.org/10.1038/s41598-022-21080-z

    Article  ADS  Google Scholar 

  29. G.I. Taylor, Experiments with rotating fluids. Proc. R. Soc. Lond. Ser. A Contain. Pap. Math. Phys. Charact. 100(703), 114–121 (1921). https://doi.org/10.1098/rspa.1921.0075

    Article  ADS  MATH  Google Scholar 

  30. I. Khan, A.U. Rahman, A. Dawar, S. Islam, A. Zaman, Second-order slip flow of a magnetohydrodynamic hybrid nanofluid past a bi-directional stretching surface with thermal convective and zero mass flux conditions. Adv. Mech. Eng. 15, 16878132221149894 (2023)

    Article  Google Scholar 

  31. N. Vijay, K. Sharma, Magnetohydrodynamic hybrid nanofluid flow over a decelerating rotating disk with Soret and Dufour effects. Multidiscip. Model. Mater. Struct. 19, 253–276 (2023)

    Article  Google Scholar 

  32. T. Hussain, H. Xu, A. Raees, Q.-K. Zhao, Unsteady three-dimensional MHD flow and heat transfer in porous medium suspended with both microorganisms and nanoparticles due to rotating disks. J. Therm. Anal. Calorim. (2022) 1–13.

  33. Z. Shah, S. Islam, T. Gul, E. Bonyah, M. Altaf Khan, The electrical MHD and Hall current impact on micropolar nanofluid flow between rotating parallel plates. Results Phys. 9, 1201–1214 (2018). https://doi.org/10.1016/j.rinp.2018.01.064

    Article  ADS  Google Scholar 

  34. C. Yin, L. Zheng, C. Zhang, X. Zhang, Flow and heat transfer of nanofluids over a rotating disk with uniform stretching rate in the radial direction. Propuls. Power Res. 6(1), 25–30 (2017). https://doi.org/10.1016/j.jppr.2017.01.004

    Article  Google Scholar 

  35. D.-H. Doh, M. Muthtamilselvan, B. Swathene, E. Ramya, Homogeneous and heterogeneous reactions in a nanofluid flow due to a rotating disk of variable thickness using HAM. Math. Comput. Simul 168, 90–110 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  36. R. Naveen Kumar, R.J. Gowda, B.J. Gireesha, B.C. Prasannakumara, Non-Newtonian hybrid nanofluid flow over vertically upward/downward moving rotating disk in a Darcy-Forchheimer porous medium. Eur. Phys. J. Spec. Top. 230, 1227–1237 (2021)

    Article  Google Scholar 

  37. Y.P. Lv, E.A. Algehyne, M.G. Alshehri, E. Alzahrani, Numerical approach towards gyrotactic microorganisms hybrid nanoliquid flow with the hall current and magnetic field over a spinning disk. Sci. Rep. 11, 8948 (2021). https://doi.org/10.1038/s41598-021-88269-6

    Article  ADS  Google Scholar 

  38. Y.R.O. Reddy, M.S. Reddy, P.S. Reddy, A.J. Chamkha, Effect of Brownian motion and thermophoresis on heat and mass transfer flow over a horizontal circular cylinder filled with nanofluid. J. Nanofluid 6, 702–710 (2017). https://doi.org/10.1166/jon.2017.1365

    Article  Google Scholar 

  39. A. Aziz, A similarity solution for laminar thermal boundary layer over a flat plate with a convective surface boundary condition. Commun. Nonlinear Sci. Numer. Simul. 14, 1064–1068 (2009)

    Article  ADS  Google Scholar 

  40. I. Tlili, N.N. Hamadneh, W.A. Khan, Thermodynamic analysis of MHD heat and mass transfer of nanofluids past a static wedge with Navier slip and convective boundary conditions. Arab. J. Sci. Eng. (2018). https://doi.org/10.1007/s13369-018-3471-0

    Article  Google Scholar 

  41. R. Ahmad, W.A. Khan, Numerical study of heat and mass transfer MHD viscous flow over a moving wedge in the presence of viscous dissipation and heat source/sink with convective boundary condition. Heat Transf. Res. 43, 17–38 (2014)

    Article  Google Scholar 

  42. A. Wakif, N.A. Shah, Hydrothermal and mass impacts of azimuthal and transverse components of Lorentz forces on reacting Von Kármán nanofluid flows considering zero mass flux and convective heating conditions, Waves Random Complex Media. (2022) 1–22.

  43. U. Khan, A. Zaib, I. Waini, A. Ishak, E.-S.M. Sherif, W.-F. Xia, N. Muhammad, Impact of Smoluchowski temperature and Maxwell velocity slip conditions on axisymmetric rotated flow of hybrid nanofluid past a porous moving rotating disk. Nanomaterials 12, 276 (2022)

    Article  Google Scholar 

  44. A. Dawar, E. Bonyah, S. Islam, A. Alshehri, Z. Shah, Theoretical analysis of Cu–H2O, Al2O3–H2O, and TiO2–H2O nanofluid flow past a rotating disk with velocity slip and convective conditions. J. Nanomater. 2021, 1–10 (2021)

    Article  Google Scholar 

  45. J. Ahmed, M. Khan, L. Ahmad, Stagnation point flow of Maxwell nanofluid over a permeable rotating disk with heat source/sink. J. Mol. Liq. 287, 110853 (2019). https://doi.org/10.1016/j.molliq.2019.04.130

    Article  Google Scholar 

  46. P. Ragupathi, T. Muhammad, S. Islam, A. Wakif, Application of Arrhenius kinetics on MHD radiative Von Kármán Casson nanofluid flow occurring in a Darcy-Forchheimer porous medium in the presence of an adjustable heat source. Phys. Scr. 96, 125228 (2021). https://doi.org/10.1088/1402-4896/AC297C

    Article  ADS  Google Scholar 

  47. T.V. Kármán, Über laminare und turbulente Reibung. ZAMM - J. Appl. Math. Mech. Z. Ang. Math. Mech. 1, 233–252 (1921). https://doi.org/10.1002/ZAMM.19210010401

    Article  MATH  Google Scholar 

  48. U. Khan, S. Bilal, A. Zaib, O.D. Makinde, A. Wakif, Numerical simulation of a nonlinear coupled differential system describing a convective flow of Casson gold–blood nanofluid through a stretched rotating rigid disk in the presence of Lorentz forces and nonlinear thermal radiation. Numer. Methods Part. Differ. Equ. 38, 308–328 (2022)

    MathSciNet  Google Scholar 

  49. A. Dawar, S. Islam, Z. Shah, S.R. Mahmuod, A passive control of casson hybrid nanofluid flow over a curved surface with alumina and copper nanomaterials: a study on sodium alginate-based fluid. J. Mol. Liq. 382, 122018 (2023)

    Article  Google Scholar 

  50. A. Dawar, T. Thumma, S. Islam, Z. Shah, Optimization of response function on hydromagnetic buoyancy-driven rotating flow considering particle diameter and interfacial layer effects: homotopy and sensitivity analysis. Int. Commun. Heat Mass Transf. 144, 106770 (2023). https://doi.org/10.1016/J.ICHEATMASSTRANSFER.2023.106770

    Article  Google Scholar 

  51. M. Mustafa, T. Hayat, A. Alsaedi, Axisymmetric flow of a nanofluid over a radially stretching sheet with convective boundary conditions. Curr. Nanosci. 8, 328–334 (2012)

    Article  ADS  Google Scholar 

  52. W. Ibrahim, D. Gamachu, Nonlinear convection flow of Williamson nanofluid past a radially stretching surface. AIP Adv. 9, 85026 (2019)

    Article  Google Scholar 

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Acknowledgements

The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University, Abha, Saudi Arabia, for funding this work through the Research Group Project under Grant Number (RGP.1/505/44).

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Authors and Affiliations

  1. Department of Basic Sciences, College of Science and Theoretical Studies, Saudi Electronic University, 11673, Jeddah-M, Riyadh, Kingdom of Saudi Arabia

    Showkat Ahmad Lone

  2. Department of Mathematics, College of Arts and Sciences, Wadi Ad Dawasir (11991), Prince Sattam Bin Abdul Aziz University, Al-Kharj, Kingdom of Saudi Arabia

    Sadia Anwar

  3. Department of Mathematics, College of Science, King Khalid University, Abha, Kingdom of Saudi Arabia

    Zehba Raizah

  4. Department of Mathematics, Faculty of Science, Jazan University, Jazan, Kingdom of Saudi Arabia

    Musawa Yahya Almusawa

  5. Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, ThungKhru, Bangkok, 10140, Thailand

    Anwar Saeed

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Lone, S.A., Anwar, S., Raizah, Z. et al. A theoretical investigation of the MHD water-based hybrid nanofluid flow over a convectively heated rotating disk surface with velocity slips and zero mass flux conditions. Eur. Phys. J. Plus 138, 866 (2023). https://doi.org/10.1140/epjp/s13360-023-04489-x

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