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Journal of Interdisciplinary Mathematics

(Since 1998)
Open Access ·Peer-reviewed·ISSN (Online): 2169-012X·ISSN (Print): 0972-0502
CiteScore 2025: 1.9 (Q2)

CiteScore 2025: 1.9 (Q2)

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Journal of Interdisciplinary Mathematics
Open Access Research Article

Influence of shape factor on the tangent hyperbolic hybrid nanofluid flow over a nonlinear stretching sheet with Cattaneo-Christov heat flux : An irreversibility analysis

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pp. 891–908Vol. 29Issue 4April 2026DOI: 10.47974/JIM-2346XML
Received:
02 Dec 2024
Published Online:
23 Mar 2026
Article type:
Research Article
Language:
EN
Article no.:
JIM-2346
Pages:
891–908

Abstract

The aim of this work is to investigate the movement of the tangent hyperbolic hybrid nanofluid across a nonlinear elastic surface under the influence of various parameters including thermal radiation and magnetic field. The principal equations of the present problem have been turned into a collection of ordinary differential equations using the appropriate similarity transformations. Then, the bvp4c solver is used to resolve them. Multiple linear regression is used to analyze engineering parameters like the friction factor. Results are shown for both spherical and platelet-shaped nanoparticles. It is shown that an increase in the volume fraction of graphene oxide nanoparticles correlates with an enhancement in the heat transfer rate. It has been found that a stronger magnetic field and more nanoparticles slow down the flow of fluid. An upsurge in the couple stress parameter is found to result in an upsurge in the creation of entropy. We find that for both cases, the friction factor increases by 7.69% as the couple stress parameter value falls between 0.5 and 3 while the rate of heat transfer rises by 19.83% for spherical nanoparticles and 18.74% for platelet nanoparticles when the thermal radiation parameter values fall between 0 to 2.5.

Keywords

Non-Newtonian fluidbvp4cMagnetic fieldCouple stressWeissenberg number

Subject Classifications

76A0576Dxx76W0576R10

References

[1] O. Pourmehran, M. Rahimi-Gorji, and D. D. Ganji, “Heat transfer and flow analysis of nanofluid flow induced by a stretching sheet in the presence of an external magnetic field,” J. Taiwan Inst. Chem. Eng., vol. 65, pp. 162–171 (2016), doi: 10.1016/j.jtice.2016.04.035.
[2] A. A. Afify, “The influence of slip boundary condition on Casson nanofluid flow over a stretching sheet in the presence of viscous dissipation and chemical reaction,” Math. Probl. Eng., vol. 2017, no. 1, Article ID 3804751 (2017), doi: 10.1155/2017/3804751.
[3] G. S. Seth, A. Bhattacharyya, R. Kumar, and A. J. Chamkha, “Entropy generation in hydromagnetic nanofluid flow over a non-linear stretching sheet with Navier’s velocity slip and convective heat transfer,” Phys. Fluids, vol. 30, no. 12 (2018), doi: 10.1063/1.5054099.
[4] G. Rasool, A. Shafiq, C. M. Khalique, and T. Zhang, “Magnetohydrodynamic Darcy–Forchheimer nanofluid flow over a nonlinear stretching sheet,” Phys. Scr., vol. 94, no. 10, pp. 105221 (2019), doi: 10.1088/1402-4896/ab18c8.
[5] S. Misra and G. Kamatam, “Effect of magnetic field, heat generation and absorption on nanofluid flow over a nonlinear stretching sheet,” Beilstein J. Nanotechnol., vol. 11, no. 1, pp. 976–990 (2020), doi: 10.3762/bjnano.11.82.
[6] R. Naveen Kumar, S. Suresha, R. P. Gowda, S. B. Megalamani, and B. C. Prasannakumara, “Exploring the impact of magnetic dipole on the radiative nanofluid flow over a stretching sheet by means of KKL model,” Pramana, vol. 95, no. 4, pp. 180 (2021), doi: 10.1007/s12043-021-02212-y.
[7] K. A. Khan, M. F. Javed, M. A. Ullah, and M. B. Riaz, “Heat and mass transport analysis for Williamson MHD nanofluid flow over a stretched sheet,” Results Phys., vol. 53, pp. 106873 (2023), doi: 10.1016/j.rinp.2023.106873.
[8] M. Jawad, N. Sadiq, and M. R. Ali, “Analysis of chemical reactive tangent hyperbolic nanofluid flow with Joule heating and motile microorganisms through stretchable surface,” BioNanoScience, vol. 14, no. 2, pp. 605–618 (2024), doi: 10.1007/s12668-023-01268-x.
[9] S. A. A. Shah, N. A. Ahammad, E. M. T. E. Din, F. Gamaoun, A. U. Awan, and B. Ali, “Bio-convection effects on prandtl hybrid nanofluid flow with chemical reaction and motile microorganism over a stretching sheet,” Nanomaterials, vol. 12, no. 13, pp. 2174 (2022), doi: 10.3390/nano12132174.
[10] U. Farooq, M. Tahir, H. Waqas, T. Muhammad, A. Alshehri, and M. Imran, “Investigation of 3D flow of magnetized hybrid nanofluid with heat source/sink over a stretching sheet,” Sci. Rep., vol. 12, no. 1, pp. 12254 (2022), doi: 10.1038/s41598-022-15658-w.
[11] P. M. Patil, B. Goudar, and M. A. Sheremet, “Tangent hyperbolic ternary hybrid nanofluid flow over a rough-yawed cylinder due to impulsive motion,” J. Taibah Univ. Sci., vol. 17, no. 1, pp. 2199664 (2023), doi: 10.1080/16583655.2023.2199664.
[12] C. M. Mohana and B. Rushi Kumar, “Shape effects of Darcy–Forchheimer unsteady three-dimensional CdTe-C/H₂O hybrid nanofluid flow over a stretching sheet with convective heat transfer,” Phys. Fluids, vol. 35, no. 9 (2023), doi: 10.1063/5.0168503.
[13] Z. H. Khan, W. A. Khan, S. M. Ibrahim, K. Swain, and Z. Huang, “Impact of multiple slips and thermal radiation on heat and mass transfer in MHD Maxwell hybrid nanofluid flow over porous stretching sheet,” Case Stud. Therm. Eng., vol. 61, pp. 104906 (2024), doi: 10.1016/j.csite.2024.104906.
[14] B. Venkateswarlu, S. Chavan, P. V. S. Narayana, and S. W. Joo, “A numerical investigation of cross-diffusion on magnetohydrodynamic Cu–Al2O3/H2O hybrid nanofluid flow over a stretching sheet with chemical reaction,” Asia-Pac. J. Chem. Eng., vol. 19, no. 1, pp. e2985 (2024), doi: 10.1002/apj.2985.
[15] W. Jamshed and A. Aziz, “Cattaneo–Christov based study of TiO2–CuO/EG Casson hybrid nanofluid flow over a stretching surface with entropy generation,” Appl. Nanoscience, vol. 8, no. 4, pp. 685–698 (2018), doi: 10.1007/s13204-018-0820-y.
[16] A. Mahdy, “Entropy generation of tangent hyperbolic nanofluid flow past a stretched permeable cylinder: variable wall temperature,” Proc. Inst. Mech. Eng. Part E: J. Process Mech. Eng., vol. 233, no. 3, pp. 570–580 (2019), doi: 10.1177/0954408918774898.
[17] H. Hanif, I. Khan, and S. Shafie, “Heat transfer exaggeration and entropy analysis in magneto-hybrid nanofluid flow over a vertical cone: a numerical study,” J. Therm. Anal. Calorim., vol. 141, no. 5, pp. 2001–2017 (2020), doi: 10.1007/s10973-020-09256-z.
[18] M. A. Alazwari, N. H. Abu-Hamdeh, and M. Goodarzi, “Entropy optimization of first-grade viscoelastic nanofluid flow over a stretching sheet by using classical Keller-box scheme,” Mathematics, vol. 9, no. 20, pp. 2563 (2021), doi: 10.3390/math9202563.
[19] J. Kayalvizhi and A. G. Vijaya Kumar, “Entropy analysis of EMHD hybrid nanofluid stagnation point flow over a porous stretching sheet with melting heat transfer in the presence of thermal radiation,” Energies, vol. 15, no. 21, pp. 8317 (2022), doi: 10.3390/en15218317.
[20] U. Farooq, H. Waqas, M. S. Aldhabani, N. Fatima, A. Alhushaybari, M. R. Ali, and T. Muhammad, “Modeling and computational framework of radiative hybrid nanofluid configured by a stretching surface subject to entropy generation: Using Keller box scheme,” Arab. J. Chem., vol. 16, no. 4, pp. 104628 (2023), doi: 10.1016/j.arabjc.2023.104628.
[21] I. Sakthi, R. Das, and P. B. A. Reddy, “Entropy generation on MHD flow of second-grade hybrid nanofluid flow over a converging/diverging channel: an application in hyperthermia therapeutic aspects,” Eur. Phys. J. Spec. Top., vol. 233, no. 6, pp. 1233–1249 (2024), doi: 10.1140/epjs/s11734-023-00947-w.
[22] K. Sakkaravarthi and P. Bala Anki Reddy, “Non-linear thermal radiation and entropy generation on MHD Casson and Williamson hybrid nanofluids across a curved stretching sheet with Cattaneo–Christov heat flux model,” Radiat. Eff. Defects Solids, vol. 179, no. 3–4, pp. 386–420 (2024), doi: 10.1080/10420150.2023.2283840.
[23] I. Ahmed, M. Alghamdi, M. Amjad, F. Aziz, T. Akbar, and T. Muhammad, “Numerical investigation of MHD flow of hyperbolic tangent nanofluid over a non-linear stretching sheet,” Heliyon, vol. 9, no. 7, pp. e17658 (2023), doi: 10.1016/j.heliyon.2023.e17658.
[24] T. Salahuddin and M. Awais, “Cattaneo–Christov flow analysis of unsteady couple stress fluid with variable fluid properties: By using Adam’s method,” Alex. Eng. J., vol. 81, pp. 64–86 (2023), doi: 10.1016/j.aej.2023.09.021.
[25] E. A. Algehyne, A. Al-Bossly, F. S. Alduais, M. Y. Almusawa, and A. Saeed, “Significance of the inclined magnetic field on the water-based hybrid nanofluid flow over a nonlinear stretching sheet,” Nanotechnology, vol. 34, no. 21, pp. 215401 (2023), doi: 10.1088/1361-6528/acbda1.
[26] P. Prashar and O. Ojjela, “Numerical investigation of ZnO–MWCNTs/ethylene glycol hybrid nanofluid flow with activation energy,” Indian J. Phys., vol. 96, no. 7, pp. 2079–2092 (2022), doi: 10.1007/s12648-021-02132-y.
[27] N. S. Akbar, A. Ebaid, and Z. H. Khan, “Numerical analysis of magnetic field effects on Eyring–Powell fluid flow towards a stretching sheet,” J. Magn. Magn. Mater., vol. 382, pp. 355–358 (2015), doi: 10.1016/j.jmmm.2015.01.088.
[28] A. M. Amer, S. A. Al Rashdi, N. I. Ghoneim, and A. M. Megahed, “Tangent hyperbolic nanofluid flowing over a stretching sheet through a porous medium with the inclusion of magnetohydrodynamic and slip impact,” Results Eng., vol. 19, pp. 101370 (2023), doi: 10.1016/j.rineng.2023.101370.

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