<p>Nanoparticles have been shown to have a wide range of real-world applications, including solar thermal systems, automotive cooling systems, and thermal energy storage. This work examines the two-dimensional nanofluid flow past a stretching cylinder, incorporating a magnetic field and Cattaneo–Christov heat flux. The significance of Xue and Hamilton–Crosser thermal conductivity models also was considered. Appropriate similarity transformations are utilized to convert the governing equations into a non-dimensional form, which are then solved numerically using the fourth-order Runge–Kutta–Fehlberg method in conjunction with the shooting technique. The prime objective of the proposed study is to optimize the heat transport rate by regression investigation with artificial neural networks, employing the Levenberg–Marquardt algorithm with appropriately structured training, testing, and validation datasets. Flow profiles and the numerical values of the rate constants are displayed in a tabular form, while the behaviour of several parameters within their range is shown via graphs. At epoch 123, the model attained optimal validation for the Hamilton model with a mean-squared error <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\left( \text {MSE} \right) $</EquationSource> <EquationSource Format="MATHML"><math> <mfenced close=")" open="("> <mtext>MSE</mtext> </mfenced> </math></EquationSource> </InlineEquation> of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$1.0921\times 10^{-10}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1.0921</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>10</mn> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation>. In contrast, the sophisticated architecture of the Xue models is evident, as it achieved a lower MSE of <InlineEquation ID="IEq3"> <EquationSource Format="TEX">${1.4117}\times {10}^{-09}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow> <mn>1.4117</mn> </mrow> <mo>×</mo> <msup> <mrow> <mn>10</mn> </mrow> <mrow> <mo>-</mo> <mn>09</mn> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation> at epoch 371.</p>

Neural network-based predictive model for heat transfer rate in magnetohydrodynamic flow over a stretching cylinder with Cattaneo–Christov heat flux

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发表日期：

2026年2月5日

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Ram Prakash Sharma,
Abhishek Sharma,
V. Vinay Kumar,
Bimal Kumar Barik

摘要

Nanoparticles have been shown to have a wide range of real-world applications, including solar thermal systems, automotive cooling systems, and thermal energy storage. This work examines the two-dimensional nanofluid flow past a stretching cylinder, incorporating a magnetic field and Cattaneo–Christov heat flux. The significance of Xue and Hamilton–Crosser thermal conductivity models also was considered. Appropriate similarity transformations are utilized to convert the governing equations into a non-dimensional form, which are then solved numerically using the fourth-order Runge–Kutta–Fehlberg method in conjunction with the shooting technique. The prime objective of the proposed study is to optimize the heat transport rate by regression investigation with artificial neural networks, employing the Levenberg–Marquardt algorithm with appropriately structured training, testing, and validation datasets. Flow profiles and the numerical values of the rate constants are displayed in a tabular form, while the behaviour of several parameters within their range is shown via graphs. At epoch 123, the model attained optimal validation for the Hamilton model with a mean-squared error $\left( \text {MSE} \right) $ $(MSE)$ of $1.0921\times 10^{-10}$ $1.0921 \times 10^{- 10}$ . In contrast, the sophisticated architecture of the Xue models is evident, as it achieved a lower MSE of ${1.4117}\times {10}^{-09}$ $1.4117 \times 10^{- 09}$ at epoch 371.