Unsteady Ternary Hybrid Nanofluid Flow with Variable Thermophysical Properties: A Physics-Informed Neural Network and Sensitivity Analysis Approach

References

[1] Abbasi, J., & Andersen, P. Ø. (2024). Physical activation functions (PAFs): An approach for more efficient induction of physics into physics-informed neural networks (PINNs). Neurocomputing, 608, 128352.

[2] Abdelkader, K., Kezzar, M., Eid, M. R., et al. (2024). Exploration of shape factor and mass suction role on heat transfer of ternary hybrid (ZrO2, MoS2, and GO) nanofluid flow in diverging channels with porous medium. Proceedings of the Institution of Mechanical Engineers, Part N: Journal of Nanomaterials, Nanoengineering and Nanosystems, 23977914251345732.

[3] Adun, H., Mukhtar, M., Adedeji, M., et al. (2021). Synthesis and application of ternary nanofluid for photovoltaic-thermal system: Comparative analysis of energy and exergy performance with single and hybrid nanofluids. Energies, 14(15), 4434.

[4] Ali, L., Islam, S., Gul, T., et al. (2017). Magnetohydrodynamics thin film fluid flow under the effect of thermophoresis and variable fluid properties. AIChE Journal, 63, 5149-5158.

[5] Cai, S., Wang, Z., Wang, S., Perdikaris, P., & Karniadakis, G. E. (2021). Physics-informed neural networks for heat transfer problems. Journal of Heat Transfer, 143(6), 060801.

[6] Choi, S. U., & Eastman, J. A. (1995). Enhancing thermal conductivity of fluids with nanoparticles. Argonne National Lab. Report, ANL/MSD/CP-84938.

[7] Ghalambaz, M., Sheremet, M. A., Khan, M. A., Raizah, Z., & Shafi, J. (2024). Physics-informed neural networks (PINNs): Application categories, trends and impact. International Journal of Numerical Methods for Heat & Fluid Flow, 34(8), 3131-3165.

[8] Grossmann, T. G., Komorowska, U. J., Latz, J., & Schönlieb, C.-B. (2024). Can physics-informed neural networks beat the finite element method? IMA Journal of Applied Mathematics, 89(1), 143-174.

[9] Islam, M. S., Islam, S., & Siddiki, M. N.-A.-A. (2023). Numerical simulation with sensitivity analysis of MHD natural convection using Cu-TiO₂-H₂O hybrid nanofluids. International Journal of Thermofluids, 20, 100509.

[10] Jama, M., Singh, T., Gamaleldin, S. M., et al. (2016). Critical review on nanofluids: Preparation, characterization, and applications. Journal of Nanomaterials, 2016, 6717624.

[11] Kakaç, S., Yazicioğlu, A. G., & Gözükara, A. C. (2011). Effect of variable thermal conductivity and viscosity on single phase convective heat transfer in slip flow. Heat and Mass Transfer, 47(8), 879-891.

[12] Le-Duc, T., Lee, S., Nguyen-Xuan, H., & Lee, J. (2024). A hierarchically normalized physics-informed neural network for solving differential equations. Engineering Applications of Artificial Intelligence, 133, 108400.

[13] Mahanthesh, B., Shehzad, S., Mackolil, J., & Shashikumar, N. (2021). Heat transfer optimization of hybrid nanomaterial using modified Buongiorno model: A sensitivity analysis. International Journal of Heat and Mass Transfer, 171, 121081.

[14] Pearson, J. (1977). Variable-viscosity flows in channels with high heat generation. Journal of Fluid Mechanics, 83(1), 191-206.

[15] Raissi, M., Perdikaris, P., & Karniadakis, G. E. (2019). Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics, 378, 686-707.

[16] Rasheed, T., Hussain, T., Anwar, M. T., et al. (2021). Hybrid nanofluids as renewable and sustainable colloidal suspensions for potential photovoltaic/thermal and solar energy applications. Frontiers in Chemistry, 9, 737033.

[17] Raza, Q., Wang, X., Li, S., Ali, B., & Shah, N. A. (2025). Enhancing thermal and entropy optimization in bioconvection Casson fluid flow between concentric disks using tri-hybrid nanoparticles. ZAMM-Journal of Applied Mathematics and Mechanics, 105(9), e70189.

[18] Sepehrnia, M., Mohammadzadeh, K., Rozbahani, M. H., Ghiasi, M. J., & Amani, M. (2024). Experimental study, prediction modeling, sensitivity analysis, and optimization of rheological behavior and dynamic viscosity of 5W30 engine oil based SiO₂/MWCNT hybrid nanofluid. Ain Shams Engineering Journal, 15(1), 102257.

[19] Shah, T. R., Koten, H., & Ali, H. M. (2020). Performance effecting parameters of hybrid nanofluids. In Hybrid Nanofluids for Convection Heat Transfer (pp. 179-213). Academic Press.

[20] Suneetha, S., Subbarayudu, K., & Reddy, P. B. A. (2022). Hybrid nanofluids development and benefits: A comprehensive review. Journal of Thermal Engineering, 8(3), 445-455.

[21] Wang, Y., Cao, Y., Huang, Z., et al. (2024). Recent advances on machine learning for computational fluid dynamics: A survey. arXiv preprint arXiv:2408.12171.

@article{1722176,
      author = {Felix John FAWEHINMI, Moses Sunday DADA},
      title = {Unsteady Ternary Hybrid Nanofluid Flow with Variable Thermophysical Properties: A Physics-Informed Neural Network and Sensitivity Analysis Approach},
      journal = {Iconic Research And Engineering Journals},
      year = {2026},
      volume = {10},
      number = {2},
      pages = {1202-1211},
      issn = {2456-8880},
      url = {https://www.irejournals.com/formatedpaper/1722176.pdf},
      abstract = {The investigation of ternary hybrid nanofluids (THNFs) has garnered significant attention due to their exceptional thermophysical properties and potential applications in advanced thermal management systems. This study presents a comprehensive numerical investigation of unsteady stagnation-point flow of a ternary hybrid nanofluid over a convectively heated sheet, incorporating temperature-dependent viscosity and thermal conductivity variations, magnetohydrodynamic (MHD) effects, Brownian motion, thermophoresis, viscous dissipation, and chemical reaction. The governing partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations using similarity transformations. Physics-Informed Neural Networks (PINNs) are employed to obtain accurate numerical solutions, with the framework incorporating the governing equations, boundary conditions, and informed initial guesses into the loss function. The thermal performance of various ternary nanofluid compositions is evaluated, with MWCNTs/Al₂O₃/TiO₂ demonstrating the highest efficiency enhancement of 15.097%. A comprehensive parametric analysis reveals that the viscosity variation parameter (Λ) exerts the most dominant influence on momentum and transport characteristics, followed by unsteadiness (β) and thermal conductivity (ε). Response Surface Methodology (RSM) coupled with Central Composite Design (CCD) establishes quadratic regression models for skin friction, Nusselt, and Sherwood numbers, with ANOVA confirming statistical significance (R² > 0.987). Sensitivity analysis quantifies the relative impact of parameters, showing that Λ positively influences all transport quantities, while ε negatively affects skin friction and Nusselt number. This study demonstrates that PINNs provide a robust, mesh-free computational framework for complex nanofluid flows, offering superior accuracy and flexibility compared to traditional numerical methods.},
      keywords = {Ternary Hybrid Nanofluid, Physics-Informed Neural Networks, Variable Viscosity, Variable Thermal Conductivity, Magnetohydrodynamics, Sensitivity Analysis, Response Surface Methodology},
      month = {August},
      doi = {https://doi.org/10.64388/IREV10I2-1722176}
  }