This research will investigate heat transfer dynamics in thinners, applying transformer model learning in analyzing Casson fluid flow with heat transport influenced by Hall currents and Darcy–Forchheimer effects. The objective is to enhance predictions of heat transfer rates in complex non-Newtonian fluid flows, where conventional models often fall short. This work is focused on the proper modeling of dissipative Casson fluids, with applications in engineering, particularly in biomedical and industrial settings where certain effects, such as Hall currents and Darcy–Forchheimer, are present. The work simplifies the complicated governing partial differential equations through the use of similarity transformations into ordinary differential equations. These equations are subsequently transformed into an optimization problem, which is solved using an innovative approach that combines transformer model learning with mean square error and the Adam optimization algorithm. Graphical results of this new modeling approach that depicted unusual characteristics for Casson fluids under examined conditions were obtained. This research highlights the integration of advanced numerical methods and transformer model learning to refine fluid behavior modeling, significantly improving the accuracy of heat transfer predictions. These advancements have substantial practical implications, offering potential enhancements in the optimization of processes within industrial and biomedical fields.
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June 2025
Research Article|
June 10 2025
Transformer model learning driven analysis of Casson fluid flow influenced by Hall currents and Darcy–Forchheimer effects Available to Purchase
Muhammad Fawad Khan
;
Muhammad Fawad Khan
a)
(Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Software, Validation, Visualization, Writing – original draft)
1
School of Information Technology and Systems, University of Canberra
, Canberra ACT 2617, Australia
a)Author to whom correspondence should be addressed: [email protected]
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Gang Hu (胡钢)
;
Gang Hu (胡钢)
(Conceptualization, Formal analysis, Resources, Validation, Visualization, Writing – review & editing)
2
School of Civil and Environmental Engineering, Harbin Institute of Technology
, Shenzhen 518055, China
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Muhammad Sulaiman
Muhammad Sulaiman
(Conceptualization, Formal analysis, Methodology, Project administration, Resources, Supervision, Validation, Writing – review & editing)
3
Department of Mathematics, Abdul Wali Khan University Mardan
, Mardan 23200, Pakistan
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Muhammad Fawad Khan
1,a)
Muhammad Sulaiman
3
1
School of Information Technology and Systems, University of Canberra
, Canberra ACT 2617, Australia
2
School of Civil and Environmental Engineering, Harbin Institute of Technology
, Shenzhen 518055, China
3
Department of Mathematics, Abdul Wali Khan University Mardan
, Mardan 23200, Pakistan
a)Author to whom correspondence should be addressed: [email protected]
Physics of Fluids 37, 063114 (2025)
Article history
Received:
February 16 2025
Accepted:
April 21 2025
Citation
Muhammad Fawad Khan, Gang Hu, Muhammad Sulaiman; Transformer model learning driven analysis of Casson fluid flow influenced by Hall currents and Darcy–Forchheimer effects. Physics of Fluids 1 June 2025; 37 (6): 063114. https://doi.org/10.1063/5.0265963
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