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. 2025 Dec 29;15(1):44795.
doi: 10.1038/s41598-025-28258-1.

Artificial neural network paradigm of magneto-thermal behavior in tangent hyperbolic hybrid-nanofluid flow

Tazeen Athar  1 , Hamid Qureshi  2 , Taseer Muhammad  3
Affiliations

Artificial neural network paradigm of magneto-thermal behavior in tangent hyperbolic hybrid-nanofluid flow

Tazeen Athar et al. Sci Rep. .

Abstract

The study considers the flow behavior of a Magnetohydrodynamic (MHD) tangent-hyperbolic hybrid-nanofluid as it flows on an exponentially stretched surface. Boundary slippage, Joule heating, changes in thermal radiation and convective effects have impacts on thermal exchange rate. The fluid used for these experiments is ethylene glycol (EG) and copper with alumina [Formula: see text] nanoparticles to enhance heat transfer. The dictating partial differential equations (PDEs) transformed into ordinary differential equations (ODEs) employing suitable similarity techniques. Artificial Intelligence (AI) based Machine Learning (ML) Levenberg Marquardt Algorithm (LMA) is used to determine the impact of parameters involved in MHD tangent hyperbolic nanofluid flow. The influence of flow rate and thermal heat transfer are studied through graphical analyses. A rise in magnetic parameter and ratio of elastic to viscous drags causes decline in flow. While the Lorentz parameter and ambient temperature difference boosts the temperature profile on rising. The ANN-LMA had mean-squared-error in the range of 7.62 × 10-11 to 4.59 × 10-10 on the six cases and also converged within 79-1000 epochs based on the experiment and good regression fits were displayed. This research is useful in paper production, cooling metal sheets, and crystal growth. The novelty lies in applying LMA-based ANN to approximate the model which has not been reported previously.

Keywords: Artificial intelligence; Exponentially stretching surface; Hybrid nanofluid; Levenberg–Marquardt algorithm; Machine learning; Magnetohydrodynamics; Neural network; Tangent hyperbolic fluid; Thermal radiation.

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Conflict of interest statement

Declarations. Competing interests: The authors declare no competing interests. Consent to Publish: The authors confirm that this manuscript has not been published elsewhere and is not under consideration by any other journal.

Figures

Fig. 1
Fig. 1
Applications of HNF.
Fig. 2
Fig. 2
Geometry of the problem.
Fig. 3
Fig. 3
LMA Neural Network.
Fig. 4
Fig. 4
Flow chart of problem evaluation.
Fig. 5
Fig. 5
Training, Validation, and Testing curves for HNF flow.
Fig. 6
Fig. 6
Training states of LMA for HNF flow.
Fig. 7
Fig. 7
Error histograms of LMA for HNF flow.
Fig. 8
Fig. 8
Regression analysis of LMA for HNF flow over stretched porous sheet.
Fig. 9
Fig. 9
Comparison curves for fitness of LMA for HNF flow.
Fig. 10
Fig. 10
AI-generated Solutions and difference curves of HNF.
Fig. 10
Fig. 10
AI-generated Solutions and difference curves of HNF.
See this image and copyright information in PMC

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