<p>The current scientific work examines a pseudo-plastic Williamson fluid over a homogenous porous media. Momentum and energy equations refer to the executive branch partial differential equations (PDE). A new transformation and symmetry analysis scaling group are applied to these PDEs to convert them into ordinary differential equations (ODEs). The numerical algorithm utilized to perform the BVP4C solver from the MATLAB series solves these ODEs. The present research explores the impact of different physical parameters on temperature and velocity distributions. The coefficient of skin friction (<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40819_2025_1870_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="26" /> </InlineMediaObject> <EquationSource Format="TEX">$C_{f_{x}}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>C</mi> <msub> <mi>f</mi> <mi>x</mi> </msub> </msub> </math></EquationSource> </InlineEquation>) and the local Nusselt number (<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40819_2025_1870_Article_IEq2.gif" Format="GIF" Height="18" Rendition="HTML" Resolution="72" Type="Linedraw" Width="29" /> </InlineMediaObject> <EquationSource Format="TEX">$N_{u_{x}}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>N</mi> <msub> <mi>u</mi> <mi>x</mi> </msub> </msub> </math></EquationSource> </InlineEquation>) are employed to illustrate graphs and table values. Furthermore, Machine Learning (ML) models adopted Multiple Linear Regression (MLR) to predict physical quantities with a <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40819_2025_1870_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="31" /> </InlineMediaObject> <EquationSource Format="TEX">$95\%$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>95</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation> accuracy. Subsequently, implementing the Levenberg-Marquardt Artificial Neural Network approach handles complex nonlinear problems, accurate predictions, optimizations, and error reduction to validate the outcomes of biomedical applications and its accuracy level of <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40819_2025_1870_Article_IEq4.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="31" /> </InlineMediaObject> <EquationSource Format="TEX">$99\%$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>99</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation>. These innovative approaches are expected to promote future developments in energy-related technology optimization, and the conclusions are more advanced than previous physical evidence and biological applications, including blood flow analysis, drug delivery systems, and cancer treatment.</p>

The Artificial Neural Network Optimization for Thermally Magnetized Williamson Fluid Flow over a Porous Surface

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发表日期：

2025年3月15日

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P. Priyadharshini,
V. Karpagam

摘要

The current scientific work examines a pseudo-plastic Williamson fluid over a homogenous porous media. Momentum and energy equations refer to the executive branch partial differential equations (PDE). A new transformation and symmetry analysis scaling group are applied to these PDEs to convert them into ordinary differential equations (ODEs). The numerical algorithm utilized to perform the BVP4C solver from the MATLAB series solves these ODEs. The present research explores the impact of different physical parameters on temperature and velocity distributions. The coefficient of skin friction ( $C_{f_{x}}$ $C_{f_{x}}$ ) and the local Nusselt number ( $N_{u_{x}}$ $N_{u_{x}}$ ) are employed to illustrate graphs and table values. Furthermore, Machine Learning (ML) models adopted Multiple Linear Regression (MLR) to predict physical quantities with a $95\%$ $95 %$ accuracy. Subsequently, implementing the Levenberg-Marquardt Artificial Neural Network approach handles complex nonlinear problems, accurate predictions, optimizations, and error reduction to validate the outcomes of biomedical applications and its accuracy level of $99\%$ $99 %$ . These innovative approaches are expected to promote future developments in energy-related technology optimization, and the conclusions are more advanced than previous physical evidence and biological applications, including blood flow analysis, drug delivery systems, and cancer treatment.