The present analysis aims to investigate the micropolar hybrid nanofluid (MHNF) over an extended curved sheet using AI-BLMS. Impacts of joule and thermal are also considered in the analysis. Nanoparticles such as MgO and Ag are utilized in ethylene glycol (EG). The novelty of this study lies in the first-time physical analysis of MHNF flow over a curved stretching sheet under the combined effects of magnetic field, thermal radiation, and Joule heating, which significantly alters momentum and heat transfer due to microrotation and curvature effects using AI-BLMS. Similarity variables are used to change the partial differential equations. The RK4 approach is used in generation of numerical data using the Mathematica software. In the optimization assessment, the stochastic AI-BLMS is used. The dataset that is used to train, validate, and test in the optimization is <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$70\%-15\%-15\%$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>70</mn> <mo>%</mo> <mo>-</mo> <mn>15</mn> <mo>%</mo> <mo>-</mo> <mn>15</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation>, respectively. With the help of MATLAB, the following filtration and evaluations were made using the produced dataset. The multidimensional interdependence of various thermophysical variables is examined. The flow rate, temperature, skin friction, and Nusselt number are shown in dependence of the variations in the relevant parameters. The velocity curve is found to be decreasing when the variable of the Casson fluid increases. The correlation coefficient <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$(R)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>R</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> 0.99203 and the mean error rate of − 0.24 in AI-BLMS are calculated with MSE = 4.1335 × e−4. Similarly, for the Nusselt number, MSE has been established as 1.5061 × e−6 when R = 0.99968 and mean error rate is 0.02%.

Artificial intelligent AI-assisted based back-propagation Levenberg–Marquardt scheme (AI-BLMS) for micropolar hybrid nanofluid flow over a curved sheet

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发表日期：

2026年2月24日

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Zeeshan,
Waris Khan,
Mohamed Kallel,
Salman Saleem,
Afnan Al Agha,
Hakim AL Garalleh

摘要

The present analysis aims to investigate the micropolar hybrid nanofluid (MHNF) over an extended curved sheet using AI-BLMS. Impacts of joule and thermal are also considered in the analysis. Nanoparticles such as MgO and Ag are utilized in ethylene glycol (EG). The novelty of this study lies in the first-time physical analysis of MHNF flow over a curved stretching sheet under the combined effects of magnetic field, thermal radiation, and Joule heating, which significantly alters momentum and heat transfer due to microrotation and curvature effects using AI-BLMS. Similarity variables are used to change the partial differential equations. The RK4 approach is used in generation of numerical data using the Mathematica software. In the optimization assessment, the stochastic AI-BLMS is used. The dataset that is used to train, validate, and test in the optimization is $70\%-15\%-15\%$ $70 % - 15 % - 15 %$ , respectively. With the help of MATLAB, the following filtration and evaluations were made using the produced dataset. The multidimensional interdependence of various thermophysical variables is examined. The flow rate, temperature, skin friction, and Nusselt number are shown in dependence of the variations in the relevant parameters. The velocity curve is found to be decreasing when the variable of the Casson fluid increases. The correlation coefficient $(R)$ $(R)$ 0.99203 and the mean error rate of − 0.24 in AI-BLMS are calculated with MSE = 4.1335 × e⁻⁴. Similarly, for the Nusselt number, MSE has been established as 1.5061 × e⁻⁶ when R = 0.99968 and mean error rate is 0.02%.