The research investigates the Casson fluid model for mixed convection flow in artificial neural networks, emphasizing non-Fourier double-diffusion theories alongside ion slip and Hall effects. The research investigates the dynamics of a Casson nanofluid within a Darcy–Forchheimer porous medium characterized by significant inertial and viscous stresses. The trained neural networks forecast velocity, temperature, and concentration profiles, offering a reliable computer substitute for traditional approaches, with achieved mean square errors (MSE) on the order of 10⁻9 to 10⁻10. The study demonstrates an inverse relationship between fluid velocity and the Schmidt number, while ion slip and Hall parameters exhibit direct correlations with vertical velocity. Furthermore, temperature profiles are directly correlated with the thermophoresis parameter (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">$Nt$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="italic">Nt</mi> </mrow> </math></EquationSource> </InlineEquation>) but inversely related to the Prandtl number <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\left( {Pr} \right)$</EquationSource> <EquationSource Format="MATHML"><math> <mfenced close=")" open="("> <mrow> <mi mathvariant="italic">Pr</mi> </mrow> </mfenced> </math></EquationSource> </InlineEquation>, Hall parameter (<InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\alpha_{\text{e}}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>α</mi> <mtext>e</mtext> </msub> </math></EquationSource> </InlineEquation>), and buoyancy ratio parameter <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$\left( {Nr} \right)$</EquationSource> <EquationSource Format="MATHML"><math> <mfenced close=")" open="("> <mrow> <mi mathvariant="italic">Nr</mi> </mrow> </mfenced> </math></EquationSource> </InlineEquation>. Concentration profiles increase with the mixed convection parameter <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$\left( \lambda \right)$</EquationSource> <EquationSource Format="MATHML"><math> <mfenced close=")" open="("> <mi>λ</mi> </mfenced> </math></EquationSource> </InlineEquation>, Hall parameter, Schmidt number <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$\left( {Sc} \right),$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mfenced close=")" open="("> <mrow> <mi mathvariant="italic">Sc</mi> </mrow> </mfenced> <mo>,</mo> </mrow> </math></EquationSource> </InlineEquation>, and thermal relaxation parameter <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$\left( {\lambda_{2} } \right).$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mfenced close=")" open="("> <msub> <mi>λ</mi> <mn>2</mn> </msub> </mfenced> <mo>.</mo> </mrow> </math></EquationSource> </InlineEquation> Neural networks utilizing backpropagation employ the Levenberg–Marquardt optimization (LMS) technique to minimize absolute errors, which are consistently contained within a range of 10⁻3 to 10⁻10, hence ensuring precision and dependability. The enhanced heat transfer properties informed by these AI-driven predictions can be utilized to develop more efficient systems in industries such as HVAC and power plants. The dataset for the proposed LMS-ANN model was partitioned into 70% for training, 15% for validation, and 15% for testing. The findings illustrate the capability of AI-driven neural networks in tackling complex, multi-parameter fluid dynamics issues and encourage additional exploration of AI-based solutions in computational fluid dynamics.

AI-enhanced modeling of thermal and mass transport in Casson fluids with non-Fourier double diffusion and Hall ion effects

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发表日期：

2026年1月7日

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Raheela Razzaq,
Shazia Habib,
Zeeshan Khan,
Bandar Almohsen,
M. N. Abrar,
Umer Farooq

摘要

The research investigates the Casson fluid model for mixed convection flow in artificial neural networks, emphasizing non-Fourier double-diffusion theories alongside ion slip and Hall effects. The research investigates the dynamics of a Casson nanofluid within a Darcy–Forchheimer porous medium characterized by significant inertial and viscous stresses. The trained neural networks forecast velocity, temperature, and concentration profiles, offering a reliable computer substitute for traditional approaches, with achieved mean square errors (MSE) on the order of 10⁻⁹ to 10⁻¹⁰. The study demonstrates an inverse relationship between fluid velocity and the Schmidt number, while ion slip and Hall parameters exhibit direct correlations with vertical velocity. Furthermore, temperature profiles are directly correlated with the thermophoresis parameter ( $Nt$ $Nt$ ) but inversely related to the Prandtl number $\left( {Pr} \right)$ $(\Pr)$ , Hall parameter ( $\alpha_{\text{e}}$ $α_{e}$ ), and buoyancy ratio parameter $\left( {Nr} \right)$ $(Nr)$ . Concentration profiles increase with the mixed convection parameter $\left( \lambda \right)$ $(λ)$ , Hall parameter, Schmidt number $\left( {Sc} \right),$ $(Sc),$ , and thermal relaxation parameter $\left( {\lambda_{2} } \right).$ $(λ_{2}) .$ Neural networks utilizing backpropagation employ the Levenberg–Marquardt optimization (LMS) technique to minimize absolute errors, which are consistently contained within a range of 10⁻³ to 10⁻¹⁰, hence ensuring precision and dependability. The enhanced heat transfer properties informed by these AI-driven predictions can be utilized to develop more efficient systems in industries such as HVAC and power plants. The dataset for the proposed LMS-ANN model was partitioned into 70% for training, 15% for validation, and 15% for testing. The findings illustrate the capability of AI-driven neural networks in tackling complex, multi-parameter fluid dynamics issues and encourage additional exploration of AI-based solutions in computational fluid dynamics.