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RESEARCH ARTICLE

Thermal and mass transport analysis of solar-driven Williamson nanofluid flow over a stretching/shrinking wedge under an inclined magnetic field and heat generation

Amir Abbas1,2* ,  Akhlaqur Rahman3 ,  Maria Gulzar1 ,  Muhammad Farman2,4,5 ,  Mohamed Ahmed Hafez6,7 ,  Evren Hincal2,8,9 ,  Sk. Arefin. Shezan10 ,  Naveed Ahmad11
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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, Turkey
3 Department of Electrical Engineering and Industrial Automation, Engineering Institute of Technology, Melbourne, Victoria, Australia
4 Department of Biostatistics and Medical Informatics, Faculty of Medicine, Karadeniz Technical University, Trabzon, Turkey
5 International Center for Interdisciplinary Research in Sciences, The University of Lahore, Lahore, Punjab, Pakistan
6 Faculty of Engineering and Quantity Surveying, INTI International University, Nilai, Negeri Sembilan, Malaysia
7 Faculty of Management, Shinawatra University, Pathum Thani, Thailand
8 Department of Mathematical Sciences, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Chennai, Tamil Nadu, India
9 Research Center of Applied Mathematics, Khazar University, Baku, Azerbaijan
10 Department of Electrical Engineering, Prince Faisal Centre for Renewable Energy Studies and Applications, Northern Border University, Arar, Northern Borders, Saudi Arabia
11 Department of Chemical and Materials Engineering, College of Engineering, Northern Border University, Arar, Northern Borders Saudi Arabia
IJOCTA, 026220097 https://doi.org/10.36922/IJOCTA026220097
Received: 28 May 2026 | Revised: 20 July 2026 | Accepted: 20 July 2026 | Published online: 21 August 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 growing energy consumption, increasing demand for efficient cooling systems, energy preservation in clean energy technology, cooling technology, and chemical engineering, and the applications of nanofluids and non-Newtonian fluids have attracted the attention of researchers and scientists in fluid mechanics. Because this demand cannot be accommodated in current systems using fluids of low thermal conductivity, fluids such as nanofluids with high thermal conductivity are used to improve cooling systems. Therefore, the combined study of the interactions among solar radiation, heat generation, and an inclined magnetic field in a two-phase Buongiorno nanofluid model coupled with a non-Newtonian Williamson fluid model, considering shrinking and stretching wedges along a flat plate and a full wedge, was conducted in the present study. The transformed differential equations were solved using MATLAB’s bvp4c solver. The results show that increasing values of the Williamson fluid parameter, heat generation parameter, and inclined magnetic field parameter lead to a decrease in the velocity field for both the shrinking and stretching wedges along a flat plate and the full wedge under an inclined magnetic force . There is an increase in the temperature profile with increasing thermophoresis parameter and solar radiation parameter. The nanoparticle volume fraction increases with increasing values of the thermophoresis parameter for both cases of a wedge along a flat plate and a full wedge. A grid-independent test was performed to ensure that the solutions are grid-independent and that convergence of the solutions was maintained. The current results are compared with existing published results, which validates the accuracy of the present solutions. 

Graphical abstract
Keywords
Williamson fluid
Shrinking wedge
Stretching wedge
Solar radiation
Inclined magnetic field
Nanofluid
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 “NBUFFR- 2026-1902-10”.
Conflict of interest
The authors declare they have no competing interests.
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An International Journal of Optimization and Control: Theories & Applications, Electronic ISSN: 2146-5703 Print ISSN: 2146-0957, Published by AccScience Publishing
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