This study investigated the three-dimensional magnetohydrodynamic flow of a ternary nanofluid (Cu-Fe3O4-GO/water) over a stretching sheet. The analysis incorporated an inclined magnetic field, suction/injection, thermal radiation, convective boundary condition and the Cattaneo–Christov heat flux model accounted for the thermal relaxation effect and eliminated the paradox of infinite heat propagation present in Fourier’s law. The governing partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations (ODEs) using similarity transformations. The resulting ODEs are solved using a semi-analytical technique Homotopy Analysis Method (HAM) renowned for its accuracy in handling nonlinear systems. To validate the HAM solution, the artificial neural network (ANN) is employed to achieve root mean square error below 0.01 and absolute error within 1%. Regression plots confirmed a strong correlation (R2 > 0.99) between HAM and ANN results demonstrating the reliability of the proposed model. The effect of key parameters—such as the magnetic field inclination angle (<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14321_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">$\Omega$</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Ω</mi> </math></EquationSource> </InlineEquation>), suction/injection parameter (S), thermal radiation parameter (Rd), and Biot number (Bi)—on velocity, temperature, skin friction, and Nusselt number are analyzed in detail. A comprehensive comparison of nanofluid, hybrid nanofluid, and ternary nanofluid performance revealed that ternary nanofluid achieved up to 35% higher heat transfer rate and 50% lower skin friction coefficient demonstrating their enhanced thermal performance. The result highlighted the significant impact of inclined magnetic field on flow asymmetry and heat transfer enhancement, with optimal performance observed at θ = 90°. This work provides a robust framework for optimizing thermal systems in aerospace, nuclear reactors, and advanced manufacturing to bridged the gap between theoretical models and practical application.

Enhanced heat transfer and flow characteristics of a ternary nanofluid under inclined magnetic field with non-Fourier law: a 3D magnetohydrodynamic analysis validated by artificial neural network

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发表日期：

2025年6月9日

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Amal F. Alharbi,
Muhammad Usman

摘要

This study investigated the three-dimensional magnetohydrodynamic flow of a ternary nanofluid (Cu-Fe₃O₄-GO/water) over a stretching sheet. The analysis incorporated an inclined magnetic field, suction/injection, thermal radiation, convective boundary condition and the Cattaneo–Christov heat flux model accounted for the thermal relaxation effect and eliminated the paradox of infinite heat propagation present in Fourier’s law. The governing partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations (ODEs) using similarity transformations. The resulting ODEs are solved using a semi-analytical technique Homotopy Analysis Method (HAM) renowned for its accuracy in handling nonlinear systems. To validate the HAM solution, the artificial neural network (ANN) is employed to achieve root mean square error below 0.01 and absolute error within 1%. Regression plots confirmed a strong correlation (R² > 0.99) between HAM and ANN results demonstrating the reliability of the proposed model. The effect of key parameters—such as the magnetic field inclination angle ( $\Omega$ $Ω$ ), suction/injection parameter (S), thermal radiation parameter (Rd), and Biot number (Bi)—on velocity, temperature, skin friction, and Nusselt number are analyzed in detail. A comprehensive comparison of nanofluid, hybrid nanofluid, and ternary nanofluid performance revealed that ternary nanofluid achieved up to 35% higher heat transfer rate and 50% lower skin friction coefficient demonstrating their enhanced thermal performance. The result highlighted the significant impact of inclined magnetic field on flow asymmetry and heat transfer enhancement, with optimal performance observed at θ = 90°. This work provides a robust framework for optimizing thermal systems in aerospace, nuclear reactors, and advanced manufacturing to bridged the gap between theoretical models and practical application.