Numerical Investigation of Jeffrey Nanofluid over a Moving Thin Needle with Exothermic Chemical Reaction: A Levenberg-Marquardt Neural Network Approach
Abstract
This study examines the heat and mass transmission properties of a Jeffrey nanofluid traveling across a moving slender needle. The main aim is to examine how essential parameters, such as Hall current, couple stress, activation energy, and thermophoresis, affect the fluid's velocity, temperature, concentration, and corresponding entropy generation. The flow configuration of a slender needle is critically pertinent to practical applications, including the thermal design of microneedles for regulated medication delivery, the aerodynamic profiling of slender structural elements in aerospace engineering, and the optimization of delicate sensor probes. With the aid of suitable similarity transformations, the equations which were meant to describe the problem, were transmuted as a framework with nonlinear ordinary equations, and then solved using the bvp4c solver. A notable discovery is that fluid velocity is hindered by augmented magnetic field strength and coupling stresses, while the temperature profile is improved by elevated viscous dissipation and thermophoresis effects. Moreover, the heat transfer rate at the surface decreases as the thermophoresis parameter increases, whereas the mass transfer rate diminishes with higher activation energy. The study indicates that entropy formation, representing energy loss, increases with heightened viscous dissipation and thermal radiation. It is found that the Sherwood number declines by 24.1% when activation energy rises from 0 to 0.8. It is found that the Nusselt number declines by 26.3% when thermophoresis parameter rises from 0 to 2. It is discovered that the friction factor raises by 2.32% when magnetic field parameter escalates from 0 to 2.
Downloads
References
Bhatti, M. M., Abbas, T., & Rashidi, M. M. “Entropy generation as a practical tool of optimisation for non-Newtonian nanofluid flow through a permeable stretching surface using SLM,” Journal of Computational Design and Engineering, 4(1), 21-28 (2017). https://doi.org/10.1016/j.jcde.2016.08.004
Amanulla, C. H., Nagendra, N., & Reddy, M. S. “Numerical simulations on magnetohydrodynamic non-Newtonian nanofluid flow over a semi-infinite vertical surface with slipeffects,” Journal of Nanofluids, 7(4), 718-730 (2018). https://doi.org/10.1166/jon.2018.1499
Goodarzi, M., Javid, S., Sajadifar, A., Nojoomizadeh, M., Motaharipour, S. H., Bach, Q. V., & Karimipour, A. “Slip velocity and temperature jump of a non-Newtonian nanofluid, aqueous solution of carboxy-methyl cellulose/aluminum oxide nanoparticles, through a microtube,” International Journal of Numerical Methods for Heat & Fluid Flow, 29(5), 1606-1628 (2019). https://doi.org/10.1108/hff-05-2018-0192
Rao, A. S., Sainath, S., Rajendra, P., & Ramu, G. “Mathematical modelling of hydromagnetic casson non-Newtonian nanofluid convection slip flow from an isothermal sphere,” Nonlinear engineering, 8(1), 645-660 (2019). https://doi.org/10.1515/nleng-2018-0016
Ahmadian, A., Bilal, M., Khan, M. A., & Asjad, M. I. “The non-Newtonian maxwell nanofluid flow between two parallel rotating disks under the effects of magnetic field,” Scientific Reports, 10(1), 17088 (2020). https://doi.org/10.1038/s41598-020-74096-8
Usman, A. H., Khan, N. S., Humphries, U. W., Shah, Z., Kumam, P., Khan, W., ... & Ullah, Z. “Development of dynamic model and analytical analysis for the diffusion of different species in non-Newtonian nanofluid swirling flow,” Frontiers in Physics, 8, 616790 (2021). https://doi.org/10.3389/fphy.2020.616790
Elgazery, N. S. “CPSM simulation of the variable properties’ role in MHD non-Newtonian micropolar nanofluid flow over a stretching porous sheet (flow filtration),” Arabian Journal for Science and Engineering, 46(8), 7661-7680 (2021). https://doi.org/10.1007/s13369-021-05489-8
Yousef, N. S., Megahed, A. M., Ghoneim, N. I., Elsafi, M., & Fares, E. “Chemical reaction impact on MHD dissipative Casson-Williamson nanofluid flow over a slippery stretching sheet through porous medium,” Alexandria Engineering Journal, 61(12), 10161-10170 (2022). https://doi.org/10.1016/j.aej.2022.03.032
Anwar, M. I., Firdous, H., Zubaidi, A. A., Abbas, N., & Nadeem, S. “Computational analysis of induced magnetohydrodynamic non-Newtonian nanofluid flow over nonlinear stretching sheet,” Progress in reaction kinetics and mechanism, 47, 14686783211072712 (2022). https://doi.org/10.1177/14686783211072712
Sharma, B. K., Kumar, A., Gandhi, R., Bhatti, M. M., & Mishra, N. K. “Entropy generation and thermal radiation analysis of EMHD Jeffrey nanofluid flow: Applications in solar energy,” Nanomaterials, 13(3), 544 (2023). https://doi.org/10.3390/nano13030544
Ashraf, M. B., Tanveer, A., & Ulhaq, S. “Effects of Cattaneo-Christov heat flux on MHD Jeffery nano fluid flow past a stretching cylinder,” Journal of Magnetism and Magnetic Materials, 565, 170154 (2023). https://doi.org/10.1016/j.jmmm.2022.170154
Zeeshan, A., Khalid, N., Ellahi, R., Khan, M. I., & Alamri, S. Z. “Analysis of nonlinear complex heat transfer MHD flow of Jeffrey nanofluid over an exponentially stretching sheet via three phase artificial intelligence and Machine Learning techniques,” Chaos, Solitons & Fractals, 189, 115600 (2024). https://doi.org/10.1016/j.chaos.2024.115600
Albaqami, N. N. “Using artificial neural network analysis to study Jeffrey nanofluid flow in cone–disk systems,” Mathematical and Computational Applications, 29(6), 98 (2024). https://doi.org/10.3390/mca29060098
Madan Kumar, R., Srinivasa Raju, R., Kumar, M. A., & Venkateswarlu, B. “A numerical study of thermal and diffusion effects on MHD Jeffrey fluid flow over a porous stretching sheet with activation energy,” Numerical Heat Transfer, Part A: Applications, 86(13), 4423-4444 (2025). https://doi.org/10.1080/10407782.2024.2319344
Butt, A. S., Anjum, A., Saeed, U. E. Z., Al Suliman, N., Alarfaj, K. K., & Souayeh, B. “Parametric Analysis of Entropy Generation in Jeffrey Nanofluid Flow Over an Exponentially Stretchable Surface with Convective Boundary Conditions and Magnetic Field Effects,” Journal of Nonlinear Mathematical Physics, 32(1), 85 (2025). https://doi.org/10.1007/s44198-025-00334-0
Upadhya, S. M., Jayachandra Babu, M., & Srinivasa Babu, K. S. “Machine Learning-Enhanced Simulation of Maxwell Nanofluid Flow: A Bayesian Neural Network Approach with Thermal Relaxation and Variable Viscosity Effects,” Journal of Applied and Computational Mechanics, 12(3), 815-827 (2025). https://doi.org/10.22055/jacm.2025.48495.5275
Kareem, R. A., Salawu, S. O., & Yan, Y. “Analysis of transient Rivlin-Ericksen fluid and irreversibility of exothermic reactive hydromagnetic variable viscosity,” J. Appl. Comput. Mech., 6(1), 26-36 (2020). https://doi.org/10.22055/jacm.2019.28216.1460
Salawu, O. “Transient analysis of radiative hydromagnetic poiseuille fluid flow of two-step exothermic chemical reaction through a porous channel with convective cooling,” Journal of Computational & Applied Research in Mechanical Engineering (JCARME), 10(1), 51-62 (2020). https://doi.org/10.22061/jcarme.2019.3986.1473
Raees, A., Raees-ul-Haq, M., & Mansoor, M. “Modeling and simulations of Buongiorno’s model for nanofluid in a microchannel with electro-osmotic effects and an exothermal chemical reaction,” Nanomaterials, 11(4), 905 (2021). https://doi.org/10.3390/nano11040905
Ahmad, U., Ashraf, M., Abbas, A., Rashad, A. M., & Nabwey, H. A. “Mixed convection flow along a curved surface in the presence of exothermic catalytic chemical reaction,” Scientific reports, 11(1), 12907 (2021). https://doi.org/10.1038/s41598-021-92409-3
Ogunsola, A. W., Oderinu, R. A., & Ohaegbue, A. D. “Entropy generation in a third-grade hydromagnetic fluid of generalised Arrhenius two-step exothermic reaction with convective cooling,” International Journal of Ambient Energy, 43(1), 8792-8801 (2022). https://doi.org/10.1080/01430750.2022.2102071
Zainal, N. A., Nazar, R., Naganthran, K., & Pop, I. “Flow and heat transfer over a permeable moving wedge in a hybrid nanofluid with activation energy and binary chemical reaction,” International Journal of Numerical Methods for Heat & Fluid Flow, 32(5), 1686-1705 (2022). https://doi.org/10.1108/hff-04-2021-0298
Ganesh, N. V., Al-Mdallal, Q. M., Kalaivanan, R., & Reena, K. “Arrhenius kinetics driven nonlinear mixed convection flow of Casson liquid over a stretching surface in a Darcian porous medium,” Heliyon, 9(6), (2023). https://doi.org/10.1016/j.heliyon.2023.e16135
Hamza, M. M., Abdulsalam, S., & Ahmad, S. K. “Time‐Dependent Magnetohydrodynamic (MHD) Flow of an Exothermic Arrhenius Fluid in a Vertical Channel with Convective Boundary Condition,” Advances in Mathematical Physics, 2023(1), 7173925 (2023). https://doi.org/10.1155/2023/7173925
Das, T. K., Paul, A., & Nath, J. M. “Endo/exothermic analysis of Casson and Maxwell quadra hybrid nanofluid flow configured by pollutant concentration with thermal and solute jump,” Journal of Taibah University for Science, 18(1), 2382940 (2024). https://doi.org/10.1080/16583655.2024.2382940
Khan, I., Chinyoka, T., Zulkifli, R., Muhammad, T., & Shaaban, A. A. “Computational study of non-Newtonian electro-osmotic flow between micro-parallel plates subject to Joule heating and exothermic reactions,” Colloid and Polymer Science, 302(6), 939 954 (2024). https://doi.org/10.1007/s00396-024-05242-1
Ullah, I. “Activation energy with exothermic/endothermic reaction and Coriolis force effects on magnetized nanomaterials flow through Darcy–Forchheimer porous space with variable features,” Waves in random and complex media, 35(1), 398-411 (2025). https://doi.org/10.1080/17455030.2021.2023779
Xin, X., Khan, I., M. Alqahtani, A., Chinyoka, T., Alroobaea, R., Zulkifli, R., & Ahmad, Z. “Numerical simulations of third-grade fluid flow with exothermic reactions in porous media-saturated vertical microchannels,” Numerical Heat Transfer, Part B: Fundamentals, 86(8), 2473-2493 (2025). https://doi.org/10.1080/10407790.2024.2345508
Waini, I., Ishak, A., & Pop, I. “Hybrid nanofluid flow past a permeable moving thin needle,” Mathematics, 8(4), 612 (2020). https://doi.org/10.3390/math8040612
Kumar, R. N., Gowda, R. P., Madhukesh, J. K., Prasannakumara, B. C., & Ramesh, G. K. “Impact of thermophoretic particle deposition on heat and mass transfer across the dynamics of Casson fluid flow over a moving thin needle,” Physica Scripta, 96(7), 075210 (2021). https://doi.org/10.1088/1402-4896/abf802
Ramesh, G. K., Madhukesh, J. K., Aly, E. H., & Pop, I. “Modified Buongiorno’s model for biomagnetic hybrid nanoliquid past a permeable moving thin needle,” International Journal of Numerical Methods for Heat & Fluid Flow, 32(11), 3551-3578 (2022). https://doi.org/10.1108/hff-10-2021-0696
Abbas, Z., Rehman, A. U., Khaliq, S., & Rafiq, M. Y. “Flow dynamics of MHD hybrid nanofluid past a moving thin needle with a temporal stability test: a Galerkin method approach,” Numerical Heat Transfer, Part B: Fundamentals, 84(3), 329-347 (2023). https://doi.org/10.1080/10407790.2023.2202882
Srinivasa Reddy, V., Kandasamy, J., & Sivanandam, S. “Joule heating, Dufour and Soret effects on MHD hybrid nanoliquid flow over a moving thin needle in a porous medium with thermal radiation,” World Journal of Engineering, 22(4), 866-875 (2025). https://doi.org/10.1108/wje-01-2024-0040
Ishak, A., Nazar, R., & Pop, I. “Boundary Layer Flow over a Continuously Moving Thin Needle ina Parallel Free Stream,” Chinese Physics Letters, 24(10), 2895 (2007). https://doi.org/10.1088/0256-307x/24/10/051
Ashraf, M. B., Tanveer, A., & Ulhaq, S. “Effects of Cattaneo-Christov heat flux on MHD Jeffery nano fluid flow past a stretching cylinder,” Journal of Magnetism and Magnetic Materials, 565, 170154 (2023). https://doi.org/10.1016/j.jmmm.2022.170154
Karthik, K., Srilatha, P., Madhukesh, J. K., Khan, U., Prasannakumara, B. C., Kumar, R., ... & Abdou, M. M. M. “Computational examination of heat and mass transfer of nanofluid flow across an inclined cylinder with endothermic/exothermic chemical reaction,” Case Studies in Thermal Engineering, 57, 104336 (2024). https://doi.org/10.1016/j.csite.2024.104336
Chen, J. L. S., & Smith, T. N. “Forced convection heat transfer from nonisothermal thin needles, 100(2), 358-362 (1978). https://doi.org/10.1115/1.3450809
Copyright (c) 2026 R. Krishnakumari, V. Sugunamma, M. Jayachandra Babu, J. Girish Kumar
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
