Entropy-optimized radiative Maxwell ternary nanofluid flow with magnetohydrodynamics and heat generation effects

Amir Abbas^1,2*, Akhlaqur Rahman³, Muhammad Farman^2,4,5, Mohamed Ahmed Hafez^6,7, Evren Hincal^2,8,9, Betty Wan Niu Voon¹⁰, Sk. A. Shezan¹¹, Naveed Ahmad¹²

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¹ Department of Mathematics, Faculty of Natural Sciences and Technology, Baba Guru Nanak University, Nankana Sahib, Punjab, Pakistan

² Department of Mathematics, Mathematics Research Center, Near East University, Mersin 10, Nicosia, Turkey

³ Department of Electrical Engineering and Industrial Automation, Engineering Institute of Technology, Melbourne Campus, Melbourne, Victoria, Australia

⁴ Faculty of Medicine, Department of Biostatistics and Medical Informatics, Karadeniz Technical University, Trabzon, Turkey

⁵ International Center for Interdisciplinary Research in Sciences, The University of Lahore, Lahore, Pakistan

⁶ Faculty of Engineering and Quantity Surveying INTI International University, Nilai, Malaysia

⁷ Faculty of Management, Shinawatra University, Bangtoey, Samkhok, Pathum Thani, Thailand

⁸ Department of Mathematical Sciences, Saveetha School of Engineering, SIMATS, Chennai, Tamil Nadu, India

⁹ Research Center of Applied Mathematics, Khazar University, Baku, Azerbaijan

¹⁰ College of Engineering Universiti Tenaga Nasional- Kajang, Kajang, Selangor, Malaysia

¹¹ Department of Electrical Engineering, Prince Faisal bin Khalid bin Sultan Research Chair in Renewable Energy Studies and Applications (PFCRE), Northern Border University, Arar, Saudi Arabia

¹² Department of Chemical and Materials Engineering, College of Engineering, Northern Border University, Arar, Saudi Arabia

IJOCTA, 026150056 https://doi.org/10.36922/IJOCTA026150056

Received: 6 April 2026 | Revised: 11 May 2026 | Accepted: 13 May 2026 | Published online: 12 June 2026

© 2026 by the Author(s). This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )

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Abstract

The present study investigates the mechanism of solar energy utilization as non-renewable energy in a ternary nanofluid flow and heat transfer system, incorporating a Maxwell non-Newtonian fluid over a linearly inclined stretching sheet at an inclination angle of π/4, with the effects of heat generation. The influence of a perpendicular magnetic field, which induces Lorentz forces, in a porous medium is also considered. In addition, suction at the plate and entropy generation analysis are incorporated to evaluate thermodynamic irreversibility in the system. The governing partial differential equations are transformed into a system of ordinary differential equations using appropriate similarity transformations. The transformed model is then solved using the bvp4c solver to obtain the final solution, and the results are presented in graphical and tabular form. The results indicate that increasing solar thermal radiation and magnetic field strength significantly improve temperature distribution within the system. Similarly, an increase in the heat generation parameter further enhances the temperature distribution. The presence of solar radiation enhances the fluid’s thermal efficiency. The proposed approach presents a novel framework for improving thermal management in next-generation solar energy technologies. The magnetic force, while influencing fluid motion, also affects the system’s thermal behavior. The results are compared at the end to assess the validity of the current solutions. The study further demonstrates that an increase in the Brinkman number results in a decrease in the Bejan number. Since the Bejan number represents the heat transfer irreversibility within the fluid, the increasing resistance, driven by the Brinkman number, directly affects it, thereby reducing the system’s overall thermodynamic efficiency. The comparison with previously published results shows strong agreement, validating the accuracy and reliability of the present model. A sensitivity analysis is also performed to evaluate the relative influence and ranking of key governing parameters on the system response.

Graphical abstract

Keywords

Ternary nanofluid

Entropy analysis

Porous media

Solar energy

Maxwell fluid

Heat generation

Magnetohydrodynamics

Funding

The authors extend their appreciation to the Deanship of Scientific Research at Northern Border University, Arar, KSA, for funding this research work through the project number “NBU-FFR-2026-1902-04.”

Conflict of interest

The authors declare they have no competing interests.

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