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<p>The research is centered on simulating the magnetohydrodynamic (MHD) flow of Fe<sub>3</sub>O<sub>4</sub>-C<sub>2</sub>H<sub>6</sub>O<sub>2</sub> nanofluid over a slender needle moving axially with a uniform velocity, aligned with the external free stream. The energy equation, based on Fourier’s law, accounts for heating effects resulting from Ohmic heating and viscous dissipation within the system. The governing equations are transformed into a system of non-dimensional ordinary differential equations, which are then tackled using unsupervised physics-informed neural networks. This approach, known for its mesh-free and robust nature, and yields results that align favorably with previously reported findings. The study reveals that fluid temperature increases with higher values of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(Mn, Ec\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>M</mi> <mi>n</mi> <mo>,</mo> <mi>E</mi> <mi>c</mi> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\alpha\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>. Additionally, the fluid experiences a lower drag force for increasing <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(Mn\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="italic">Mn</mi> </mrow> </math></EquationSource> </InlineEquation> when the needle is fixed, while a higher drag force in the opposite direction is observed for the case <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(e=0.5\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>e</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </math></EquationSource> </InlineEquation>.</p>

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Unsupervised learning exploration of the boundary layer flow of nanofluid over a needle

  • 期刊论文

  • 发表日期：

    2025年7月4日

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  • Himanshu Upreti,
  • Ziya Uddin,
  • Mohd Vaseem,
  • Sai Ganga

摘要

The research is centered on simulating the magnetohydrodynamic (MHD) flow of Fe3O4-C2H6O2 nanofluid over a slender needle moving axially with a uniform velocity, aligned with the external free stream. The energy equation, based on Fourier’s law, accounts for heating effects resulting from Ohmic heating and viscous dissipation within the system. The governing equations are transformed into a system of non-dimensional ordinary differential equations, which are then tackled using unsupervised physics-informed neural networks. This approach, known for its mesh-free and robust nature, and yields results that align favorably with previously reported findings. The study reveals that fluid temperature increases with higher values of \(Mn, Ec\) M n , E c and \(\alpha\) α . Additionally, the fluid experiences a lower drag force for increasing \(Mn\) Mn when the needle is fixed, while a higher drag force in the opposite direction is observed for the case \(e=0.5\) e = 0.5 .