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Thermal scrutinization of time-dependent flow of nanoparticles over a rotating sphere with autocatalytic chemical reaction

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Abstract

The idea of this work is to explore the impact of endothermic and exothermic chemical reactions on time-dependent magnetohydrodynamic nanomaterial flow, heat and mass transfer characteristics induced by a rotating sphere. Implementing combined influence of chemical reaction and activation energy is vital for improving the efficiency of thermal transmission processes in different industrial applications including energy production, pollutant control system, material processing, etc. Owing to its usage, this investigation aims to examine the influence of endothermic, exothermic reactions and activation energy on the flow of Magnetohydrodynamic over a rotating sphere with the nanoparticles that contains a mixture of water and titanium oxide. Furthermore, this investigation studies the influence of activation energy on both heat and mass transfer in fluid systems. The objective is to boost our insight into difficult problems, which could have real-world usages in areas including combustion engines. The PDEs were transformed into ODE via applying similarity variables and then solved using the BVP4c technique. This study shows that the fluid temperature reduces the reaction rate and improves the activation energy for an exothermic reaction. Also, in the case of an endothermic reaction, the fluid temperature increases the reaction rate and reduces the activation energy. Further, in exothermic reactions, the heat distribution rate is higher than endothermic reactions, considering activation energy and solid volume fraction while the mass transfer rate declines for improved values of these two factors.

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Data Availability Statement

The datasets used and/or analyzed during the current study are available from the corresponding author upon reasonable request. The manuscript has associated data in a data repository.

References

  1. S.A.A. Shah, N.A. Ahammad, E.M.T.E. Din, F. Gamaoun, A.U. Awan, B. Ali, Bio-convection effects on prandtl hybrid nanofluid flow with chemical reaction and motile microorganism over a stretching sheet. Nanomaterials 12, 2174 (2022)

    Article  Google Scholar 

  2. K. Raghunath, Study of heat and mass transfer of an unsteady magnetohydrodynamic (MHD) nanofluid flow past a vertical porous plate in the presence of chemical reaction Radiation and Soret Effects. J. Nanofluids. 12, 767–776 (2023)

    Article  Google Scholar 

  3. S.A. Hussein, S.E. Ahmed, A.A.M. Arafa, Electrokinetic peristaltic bioconvective Jeffrey nanofluid flow with activation energy for binary chemical reaction, radiation and variable fluid properties. ZAMM J. Appl. Math. Mech./Z. Angew. Math. Mech. 103, e202200284 (2023)

    Article  MathSciNet  Google Scholar 

  4. N. Acharya, R. Bag, P.K. Kundu, Unsteady bioconvective squeezing flow with higher-order chemical reaction and second-order slip effects. Heat Transf. 50, 5538–5562 (2021)

    Article  Google Scholar 

  5. R.S. Varun Kumar, P. Gunderi Dhananjaya, R. Naveen Kumar, R.J. Punith Gowda, B.C. Prasannakumara, Modeling and theoretical investigation on Casson nanofluid flow over a curved stretching surface with the influence of magnetic field and chemical reaction. Int. J. Comput. Methods Eng. Sci. Mech. 23, 12–19 (2022)

    Article  MathSciNet  Google Scholar 

  6. J.K. Madhukesh, G.K. Ramesh, R.S. Varun Kumar, B.C. Prasannakumara, M. Kbiri Alaoui, Computational study of chemical reaction and activation energy on the flow of Fe3O4-Go/water over a moving thin needle: theoretical aspects. Comput. Theoret. Chem. 1202, 113306 (2021)

    Article  Google Scholar 

  7. R.J. Punith Gowda, I.E. Sarris, R. Naveen Kumar, R. Kumar, B.C. Prasannakumara, A three-dimensional non-newtonian magnetic fluid flow induced due to stretching of the flat surface with chemical reaction. J. Heat Transf. 144, 113602 (2022)

    Article  Google Scholar 

  8. F. Alzahrani, R.J.P. Gowda, R.N. Kumar, M.I. Khan, Dynamics of thermosolutal Marangoni convection and nanoparticle aggregation effects on Oldroyd-B nanofluid past a porous boundary with homogeneous-heterogeneous catalytic reactions. J. Indian Chem. Soc. 99, 100458 (2022)

    Article  Google Scholar 

  9. A.M. Obalalu, O.A. Ajala, A.T. Adeosun, A.O. Akindele, O.A. Oladapo, O.A. Olajide, A. Peter, Significance of variable electrical conductivity on non-Newtonian fluid flow between two vertical plates in the coexistence of Arrhenius energy and exothermic chemical reaction. Part. Differ. Equ. Appl. Math. 4, 100184 (2021)

    Google Scholar 

  10. S.E. Ahmed, A.A.M. Arafa, S.A. Hussein, Bioconvective flow of a variable properties hybrid nanofluid over a spinning disk with Arrhenius activation energy Soret and Dufour impacts. Numer. Heat Transf. Part A Appl. 85, 900–922 (2024)

    Article  ADS  Google Scholar 

  11. L. Ali, B. Ali, X. Liu, S. Ahmed, M.A. Shah, Analysis of bio-convective MHD Blasius and Sakiadis flow with Cattaneo-Christov heat flux model and chemical reaction. Chin. J. Phys. 77, 1963–1975 (2022)

    Article  MathSciNet  Google Scholar 

  12. M. Jawad, M.K. Hameed, K.S. Nisar, A.H. Majeed, Darcy-Forchheimer flow of maxwell nanofluid flow over a porous stretching sheet with Arrhenius activation energy and nield boundary conditions. Case Stud. Therm. Eng. 44, 102830 (2023)

    Article  Google Scholar 

  13. K. Sudarmozhi, D. Iranian, I. Khan, J. Alzahrani, A.S. Al-johani, S.M. Eldin, Double diffusion in a porous medium of MHD Maxwell fluid with thermal radiation, heat generation and chemical reaction. Case Stud. Therm. Eng. 43, 102700 (2023)

    Article  Google Scholar 

  14. S. Li, R. Saadeh, J.K. Madhukesh, U. Khan, G.K. Ramesh, A. Zaib, B.C. Prasannakumara, R. Kumar, A. Ishak, E.-S.M. Sherif, Aspects of an induced magnetic field utilization for heat and mass transfer ferromagnetic hybrid nanofluid flow driven by pollutant concentration. Case Stud. Therm. Eng. 53, 103892 (2024)

    Article  Google Scholar 

  15. A.M. Obalalu, O.A. Ajala, A.O. Akindele, S. Alao, A. Okunloye, Effect of melting heat transfer on electromagnetohydrodynamic non-newtonian nanofluid flow over a riga plate with chemical reaction and arrhenius activation energy. Eur. Phys. J. Plus. 136, 891 (2021)

    Article  Google Scholar 

  16. M. Qayyum, S. Afzal, M.R. Ali, M. Sohail, N. Imran, G. Chambashi, Unsteady hybrid nanofluid (UO2, MWCNTs/blood) flow between two rotating stretchable disks with chemical reaction and activation energy under the influence of convective boundaries. Sci. Rep. 13, 6151 (2023)

    Article  ADS  Google Scholar 

  17. A.M. Obalalu, Heat and mass transfer in an unsteady squeezed Casson fluid flow with novel thermophysical properties: analytical and numerical solution. Heat Transf. 50, 7988–8011 (2021)

    Article  Google Scholar 

  18. G.R. Manohar, P. Venkatesh, B.J. Gireesha, J.K. Madhukesh, G.K. Ramesh, Performance of water, ethylene glycol, engine oil conveying SWCNT-MWCNT nanoparticles over a cylindrical fin subject to magnetic field and heat generation. Int. J. Model. Simul. 42, 936–945 (2022)

    Article  Google Scholar 

  19. G. Sowmya, R.S. Varun Kumar, M.D. Alsulami, B.C. Prasannakumara, Thermal stress and temperature distribution of an annular fin with variable temperature-dependent thermal properties and magnetic field using DTM-Pade approximant. Waves Random Complex Med. 0, 1–29 (2022)

  20. R.N. Kumar, F. Gamaoun, A. Abdulrahman, J.S. Chohan, R.J.P. Gowda, Heat transfer analysis in three-dimensional unsteady magnetic fluid flow of water-based ternary hybrid nanofluid conveying three various shaped nanoparticles: a comparative study. Int. J. Mod. Phys. B 36, 2250170 (2022)

    Article  ADS  Google Scholar 

  21. W. Jamshed, R.J.P. Gowda, R.N. Kumar, B.C. Prasannakumara, K.S. Nisar, O. Mahmoud, A. Rehman, A.A. Pasha, Entropy production simulation of second-grade magnetic nanomaterials flowing across an expanding surface with viscidness dissipative flux. Nanotechnol. Rev. 11, 2814–2826 (2022)

    Article  Google Scholar 

  22. G. Sowmya, R.S.V. Kumar, M.J.Y. Banu, Thermal performance of a longitudinal fin under the influence of magnetic field using Sumudu transform method with pade approximant (STM-PA). ZAMM J. Appl. Math. Mech. Z. Angew. Math. Mech. 103, e202100526 (2023)

    Article  MathSciNet  Google Scholar 

  23. H. Dessie, N. Kishan, MHD effects on heat transfer over stretching sheet embedded in porous medium with variable viscosity, viscous dissipation and heat source/sink. Ain Shams Eng. J. 5, 967–977 (2014)

    Article  Google Scholar 

  24. P.D. Mininni, D.C. Montgomery, L. Turner, Hydrodynamic and magnetohydrodynamic computations inside a rotating sphere. New J. Phys. 9, 303 (2007)

    Article  ADS  Google Scholar 

  25. M. Turkyilmazoglu, Numerical and analytical solutions for the flow and heat transfer near the equator of an MHD boundary layer over a porous rotating sphere. Int. J. Therm. Sci. 50, 831–842 (2011)

    Article  Google Scholar 

  26. P.M. Patil, B. Goudar, Impact of impulsive motion on the Eyring-Powell nanofluid flow across a rotating sphere in MHD convective regime: entropy analysis. J. Magn. Magn. Mater. 571, 170590 (2023)

    Article  Google Scholar 

  27. S.A. Lone, S. Anwar, Z. Raizah, P. Kumam, T. Seangwattana, A. Saeed, Analysis of the time-dependent magnetohydrodynamic Newtonian fluid flow over a rotating sphere with thermal radiation and chemical reaction. Heliyon 9, e17751 (2023)

    Article  Google Scholar 

  28. N. Acharya, F. Mabood, I.A. Badruddin, Thermal performance of unsteady mixed convective Ag/MgO nanohybrid flow near the stagnation point domain of a spinning sphere. Int. Commun. Heat Mass Transf. 134, 106019 (2022)

    Article  Google Scholar 

  29. U. Khan, R. Naveen Kumar, A. Zaib, B.C. Prasannakumara, A. Ishak, A.M. Galal, R.J. Punith Gowda, Time-dependent flow of water-based ternary hybrid nanoparticles over a radially contracting/expanding and rotating permeable stretching sphere. Therm. Sci. Eng. Progr. 36, 101521 (2022)

    Article  Google Scholar 

  30. N. Acharya, S. Maity, P.K. Kundu, Entropy generation optimization of unsteady radiative hybrid nanofluid flow over a slippery spinning disk. Proc. Inst. Mech. Eng. C J. Mech. Eng. Sci. 236, 6007–6024 (2022)

    Article  Google Scholar 

  31. U. Khan, S. Ahmad, A. Hayyat, I. Khan, K.S. Nisar, D. Baleanu, On the Cattaneo-Christov heat Flux model and oham analysis for three different types of nanofluids. Appl. Sci. 10, 886 (2020)

    Article  Google Scholar 

  32. J.K. Madhukesh, R. Naveen Kumar, R.J. Punith Gowda, B.C. Prasannakumara, G.K. Ramesh, M. Ijaz Khan, S. Ullah Khan, Y.-M. Chu, Numerical simulation of AA7072-AA7075/water-based hybrid nanofluid flow over a curved stretching sheet with Newtonian heating: A non-Fourier heat flux model approach. J. Mol. Liq. 335, 116103 (2021)

    Article  Google Scholar 

  33. S.U.S. Choi, J.A. Eastman, Enhancing Thermal Conductivity of Fluids with Nanoparticles (Argonne National Lab. (ANL), Argonne, 1995)

    Google Scholar 

  34. J.K. Madhukesh, B.C. Prasannakumara, U. Khan, S. Madireddy, Z. Raizah, A.M. Galal, Time-dependent stagnation point flow of water conveying titanium dioxide nanoparticle aggregation on rotating sphere object experiencing thermophoresis particle deposition effects. Energies 15, 4424 (2022)

    Article  Google Scholar 

  35. P.M. Patil, S.H. Doddagoudar, H.F. Shankar, Influence of nonlinear thermal radiation on mixed convective hybrid nanofluid flow about a rotating sphere. Heat Transf. 51, 5874–5895 (2022)

    Article  Google Scholar 

  36. P.M. Patil, S. Benawadi, The mixed convection flow of a Williamson nanoliquid over a rotating sphere with the aspects of activation energy. Int. J. Model. Simul. 44, 31–43 (2024)

    Article  Google Scholar 

  37. A.M. Obalalu, T. Oreyeni, A. Abbas, M.A. Memon, U. Khan, E.-S.M. Sherif, A.M. Hassan, I. Pop, Implication of electromagnetohydrodynamic and heat transfer analysis in nanomaterial flow over a stretched surface: applications in solar energy. Case Stud. Therm. Eng. 49, 103381 (2023)

    Article  Google Scholar 

  38. A. Malvandi, The unsteady flow of a nanofluid in the stagnation point region of a time-dependent rotating sphere. Therm. Sci. 19, 1603–1612 (2015)

    Article  Google Scholar 

  39. A. Dawar, N. Acharya, Unsteady mixed convective radiative nanofluid flow in the stagnation point region of a revolving sphere considering the influence of nanoparticles diameter and nanolayer. J. Indian Chem. Soc. 99, 100716 (2022)

    Article  Google Scholar 

  40. B.K. Sharma, R. Gandhi, N.K. Mishra, Q.M. Al-Mdallal, Entropy generation minimization of higher-order endothermic/exothermic chemical reaction with activation energy on MHD mixed convective flow over a stretching surface. Sci. Rep. 12, 17688 (2022)

    Article  ADS  Google Scholar 

  41. G.K. Ramesh, J.K. Madhukesh, N. Ali Shah, S.-J. Yook, Flow of hybrid CNTs past a rotating sphere subjected to thermal radiation and thermophoretic particle deposition. Alex. Eng. J. 64, 969–979 (2023)

    Article  Google Scholar 

  42. S.P.A. Devi, S.S.U. Devi, Numerical investigation of hydromagnetic hybrid Cu–Al2O3/water nanofluid flow over a permeable stretching sheet with suction. Int. J. Nonlinear Sci. Numer. Simul. 17, 249–257 (2016)

    Article  Google Scholar 

  43. I. Waini, U. Khan, A. Zaib, A. Ishak, I. Pop, Inspection of TiO2–CoFe2O4 nanoparticles on MHD flow toward a shrinking cylinder with radiative heat transfer. J. Mol. Liq. 361, 119615 (2022)

    Article  Google Scholar 

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Acknowledgements

This work has been funded by the Universiti Kebangsaan Malaysia project number “DIP-2023-005”. Also, the authors thank the KKU research unit for the financial and administrative support under Grant Number 574 for year 44.

Author information

Authors and Affiliations

  1. Computational Science lab, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Bengaluru, India

    P. Nimmy, K. V. Nagaraja & J. K. Madhukesh

  2. Department of Mathematical Sciences, Augustine University Ilara-Epe, Lagos, Nigeria

    A. M. Obalalu

  3. Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, UKM, Bangi, 43600, Selangor, Malaysia

    Umair Khan & Anuar Ishak

  4. Department of Mathematics, Faculty of Science, Sakarya University, Serdivan/Sakarya, 54050, Turkey

    Umair Khan

  5. Department of Computer Science and Mathematics, Lebanese American University, Byblos, 1401, Lebanon

    Umair Khan

  6. Department of Mechanical Engineering, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Bengaluru, India

    D. Sriram

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

    Taseer Muhammad

  8. Department of Mechanical Engineering and University Centre for Research and Development, Chandigarh University, Mohali, 140413, Punjab, India

    Raman Kumar

  9. Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj, 11942, Saudi Arabia

    M. Modather M. Abdou

  10. Department of Mathematics, Faculty of Science, Aswan University, Aswan, 81528, Egypt

    M. Modather M. Abdou

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  1. P. Nimmy
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  2. A. M. Obalalu
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  4. J. K. Madhukesh
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Contributions

PN, AMO, and KVN contributed to conceptualization, methodology, software, formal analysis, validation, and writing—original draft. JKM, UK, and MMMA contributed to writing—original draft, data curation, investigation, visualization, software, and validation. AI contributed to conceptualization, writing—review and editing, supervision, resources, and writing—original draft. DS, RK, and TM contributed to validation, writing review and editing, software, and writing—original draft.

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Correspondence to Umair Khan.

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Nimmy, P., Obalalu, A.M., Nagaraja, K.V. et al. Thermal scrutinization of time-dependent flow of nanoparticles over a rotating sphere with autocatalytic chemical reaction. Eur. Phys. J. Plus 139, 291 (2024). https://doi.org/10.1140/epjp/s13360-024-05081-7

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