<p>This work investigates the radiative reactive flow of Williamson fluid over a Riga plate, considering thermophoresis, heat generation, variable chemical reactions, and material viscosity. The main intention is to compute fluid velocity, temperature, and concentration under these conditions. It surpasses conventional methods in terms of efficiency and precision by employing artificial neural networks. The validity of the results has been established utilizing visual comparisons and numerical simulations, which confirm the robustness and reliability of the proposed scheme. The fluid dynamics problem is resolved by implementing a systematic design methodology incorporating training, testing, and validation. The neural network architecture is refined to acquire knowledge of patterns, and the model's performance and ability to generalize across a range of scenarios are evaluated. As a litmus test, validation against a reference dataset is implemented. The intricate interaction of flow model parameters is elucidated through visual representations, which offer profound insights into the behavior of the fluid system. The range includes the absolute error values attained throughout the testing, validation, and training phases as <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14031_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="97" /> </InlineMediaObject> <EquationSource Format="TEX">\(10^{ - 03} - 10^{ - 08}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>03</mn> </mrow> </msup> <mo>-</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>08</mn> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation>. The mean-squared error values for Cases 1–4, namely horizontal velocity, vertical velocity, temperature, and concentration, all fall within the interval <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14031_Article_IEq2.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="97" /> </InlineMediaObject> <EquationSource Format="TEX">\(10^{ - 09} - 10^{ - 10}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>09</mn> </mrow> </msup> <mo>-</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>10</mn> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation>. Maximum gradient values are observed in the range of <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14031_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="39" /> </InlineMediaObject> <EquationSource Format="TEX">\(10^{ - 08}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>08</mn> </mrow> </msup> </math></EquationSource> </InlineEquation>, whereas error histograms are observed between <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14031_Article_IEq4.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="65" /> </InlineMediaObject> <EquationSource Format="TEX">\(- 1.4e^{ - 05}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>-</mo> <mn>1.4</mn> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mn>05</mn> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation> to <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14031_Article_IEq5.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="65" /> </InlineMediaObject> <EquationSource Format="TEX">\(- 8.1e^{ - 06}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>-</mo> <mn>8.1</mn> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mn>06</mn> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation>.</p>

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Modeling of chemically reactive fluid dynamics with thermal effect and energy source through a magnetized medium

  • Shazia Habib,
  • Saleem Nasir,
  • Zeeshan Khan,
  • Abdallah S. Berrouk,
  • Saeed Islam,
  • Asim Aamir

摘要

This work investigates the radiative reactive flow of Williamson fluid over a Riga plate, considering thermophoresis, heat generation, variable chemical reactions, and material viscosity. The main intention is to compute fluid velocity, temperature, and concentration under these conditions. It surpasses conventional methods in terms of efficiency and precision by employing artificial neural networks. The validity of the results has been established utilizing visual comparisons and numerical simulations, which confirm the robustness and reliability of the proposed scheme. The fluid dynamics problem is resolved by implementing a systematic design methodology incorporating training, testing, and validation. The neural network architecture is refined to acquire knowledge of patterns, and the model's performance and ability to generalize across a range of scenarios are evaluated. As a litmus test, validation against a reference dataset is implemented. The intricate interaction of flow model parameters is elucidated through visual representations, which offer profound insights into the behavior of the fluid system. The range includes the absolute error values attained throughout the testing, validation, and training phases as \(10^{ - 03} - 10^{ - 08}\) 10 - 03 - 10 - 08 . The mean-squared error values for Cases 1–4, namely horizontal velocity, vertical velocity, temperature, and concentration, all fall within the interval \(10^{ - 09} - 10^{ - 10}\) 10 - 09 - 10 - 10 . Maximum gradient values are observed in the range of \(10^{ - 08}\) 10 - 08 , whereas error histograms are observed between \(- 1.4e^{ - 05}\) - 1.4 e - 05 to \(- 8.1e^{ - 06}\) - 8.1 e - 06 .