This study represents a boundary layer flow and heat transfer analysis of an incompressible Casson nanofluid suspended within a Darcy–Forchheimer porous medium and subjected to electro-osmotic and electromagnetic forces. The physical model incorporates nonlinear effects including magnetic field effects, Joule heating, viscous dissipation and Newtonian heating contributions. Utilizing similarity transformations, the governing partial differential equations transformed into coupled nonlinear ordinary differential equations, valid for the semi-infinite domain. Synthetic datasets for velocity and temperature profiles were created in MATHEMATICA by varying the key parameters including, electric parameter E1, Casson parameter β, permeability parameter Da, local Reynolds number <InlineEquation ID="IEq1"> <EquationSource Format="TEX">${R\text{e}}_{\widetilde{\text{x}}}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mrow> <mi>R</mi> <mtext>e</mtext> </mrow> <mover accent="true"> <mtext>x</mtext> <mo stretchy="true">~</mo> </mover> </msub> </math></EquationSource> </InlineEquation>, Eckert number Ec and Newtonian heating parameter γ. The datasets are utilized to construct a supervised neural network trained via the Levenberg–Marquardt backpropagation scheme (LMBS), to yield a reasonable accuracy and computational efficiency. The performance measures for the synthetic datasets were documented using mean squared error (MSE), regression statistics and error diagnostics. The proposed method proved stable in terms of performance with regard to absolute error where, for example, the absolute error corresponded to a decrease from 10–02 to 10–09 as indicated by the number of iterations. Via thorough analysis of the Casson nanofluid, it is observed that the velocity elevates with the increased values of electric parameter, permeability parameter and Reynold number relative to stretching velocity, while it decreases for the increased values of Casson fluid parameter. The temperature profile demonstrates an increasing trend with the increased values of Eckert number, electric parameter, permeability parameter and non-Newtonian heating parameter.

Machine learning-based analysis of Casson nanofluid flow and heat transfer in a Porous Darcy–Forchheimer framework

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发表日期：

2025年9月22日

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Zahoor Shah,
Bouthaina Dammak,
Wajeeha Naeem,
Hafedh Mahmoud Zayani,
Mohamed Medani,
Afef Dhahbi

摘要

This study represents a boundary layer flow and heat transfer analysis of an incompressible Casson nanofluid suspended within a Darcy–Forchheimer porous medium and subjected to electro-osmotic and electromagnetic forces. The physical model incorporates nonlinear effects including magnetic field effects, Joule heating, viscous dissipation and Newtonian heating contributions. Utilizing similarity transformations, the governing partial differential equations transformed into coupled nonlinear ordinary differential equations, valid for the semi-infinite domain. Synthetic datasets for velocity and temperature profiles were created in MATHEMATICA by varying the key parameters including, electric parameter E₁, Casson parameter β, permeability parameter Da, local Reynolds number ${R\text{e}}_{\widetilde{\text{x}}}$ ${R e}_{\tilde{x}}$ , Eckert number Ec and Newtonian heating parameter γ. The datasets are utilized to construct a supervised neural network trained via the Levenberg–Marquardt backpropagation scheme (LMBS), to yield a reasonable accuracy and computational efficiency. The performance measures for the synthetic datasets were documented using mean squared error (MSE), regression statistics and error diagnostics. The proposed method proved stable in terms of performance with regard to absolute error where, for example, the absolute error corresponded to a decrease from 10^–02 to 10^–09 as indicated by the number of iterations. Via thorough analysis of the Casson nanofluid, it is observed that the velocity elevates with the increased values of electric parameter, permeability parameter and Reynold number relative to stretching velocity, while it decreases for the increased values of Casson fluid parameter. The temperature profile demonstrates an increasing trend with the increased values of Eckert number, electric parameter, permeability parameter and non-Newtonian heating parameter.