Statistical analysis of 3D MHD Williamson ternary nanofluid flow and heat transfer behaviour over a bilinear horizontally stretching sheet with activation energy, heat generation and Soret–Dufour effects
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Pavani Guntaka
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M. Changal Raju
Abstract
This study investigates the non-transient three-dimensional MHD boundary layer behaviour of a non-Newtonian Williamson ternary nanofluid over a stretching horizontal sheet. The ternary nanofluid consists of Cu, TiO2, and Fe3O4 nanoparticles suspended in propylene glycol base fluid. Key physical Parametric effects are considered involve a Magnetic field acting in the transverse direction, chemical reaction process influenced by activation energy, Soret and Dufour effects, and heat generation or absorption. To analyse the system, the governing set of non-linear PDEs for the flow, heat, and mass transport have been simplified into a system of ordinary differential equations by similarity transformations. These equations are numerically Solved through MATLAB’s boundary value solver, bvp4c with the shooting method. Furthermore, Response Surface Methodology (RSM) is used to determine parameter sensitivity and show the cumulative effects of key factors.
The findings show that greater Weissenberg numbers enhance both tangential and transverse velocities due to viscoelastic characteristics. Increasing porosity improves flow penetration and momentum dispersion. Thermal radiation and heat source enhance fluid temperature, but the Dufour effect cools through concentration-induced heat transfer. Quantitative findings from RSM indicate up to 11.6 % improvement in tangential velocity and 9.8 % temperature enhancement with higher Weissenberg and radiation parameters, while concentration decreases by 7.4 % under stronger chemical reaction effects. Statistical analysis via RSM and ANOVA confirms excellent model predictability, with R2 values exceeding 97 % for all responses, reinforcing the reliability of the results. This comprehensive model provides a realistic depiction of tri-hybrid nanofluid dynamics under coupled thermal, chemical, and electromagnetic impacts. It has important implications for advanced thermal systems, energy-efficient reactors, and magneto-thermal flow control technologies.
Acknowledgments
I would like to express my sincere gratitude to Prof. S.V.K. Varma, retired from Sri Venkateswara University, Tirupati, for his valuable guidance, insightful suggestions, and continuous support throughout my research journey. His encouragement and expertise were instrumental in shaping this work and bringing it to completion.
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Research ethics: Not applicable.
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Informed consent: Not applicable.
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Author contributions: P.G. = Pavani Guntaka, Prof.M. Changal Raju = M.C. Raju. M.C.R. sir conceived the problem, developed the mathematical model, and supervised the work. P.G. performed numerical simulations and analysis. Both authors actively participated in all stages of this research, including conceptualization, investigation, data curation, validation, writing and reviewing. All authors have read and approved the final manuscript for publication.
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Use of Large Language Models, AI and Machine Learning Tools: The authors did not use any type of large language models, artificial intelligence, or machine learning tools in the preparation of this manuscript.
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Conflict of interest: The authors declare that they have no conflict of interest.
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Research funding: This research did not receive any specific grant or external funding.
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Data availability: The data sets generated and analysed during the current study are included within the article. Additional details can be provided by the corresponding author upon reasonable request.
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