<p>By virtue of significant thermal properties, nanofluids have much importance in medical field, pharmaceutical arrangements, electric batteries, chemical engineering areas and industrial heating and cooling processes. This study explores the changing effects of three-dimensional (3D) flow of (WNFM). Due to shear thinning feature of WNFM, this plays a vital role in chemical industries, plastic industries, oil industries, biotechnology and graphic designing. Modeled arrangement of PDEs is transfigured to arrangement of ordinary differential equations (ODEs) via similarity transformation. System of ODEs is then coded into Mathematica software. Numerical dataset is obtained by applying ND-Solve technique. Numerical dataset is then transferred into MATLAB for graphical study. Obtained system of ODEs is numerically solved by classy Levenberg–Marquardt backpropagation scheme (LMBS) joined with neural networks (NNs) of artificial intelligence (AI). Results are gauged through performance graphs under NNs of AI in LMBS. Engagement of regression illustrations (RIs), mean-squared errors (MEs) training state analysis (TSA), and histogram analysis of errors (AHEs) is considered for accuracy and convergence of results. Along temperature, concentration, bioconvection, and velocity profiles, various parameters are analyzed including Lewis number, thermophoresis parameter, Prandtl number, magnetic parameter, parameter of temperature ratio, thermal Biot number, parameter of chemical reaction, and parameter of Brownian motion. The absolute error factor ranges in the bracket of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\left[{10}^{-6}-{10}^{-3}\right]$</EquationSource> <EquationSource Format="MATHML"><math> <mfenced close="]" open="["> <msup> <mrow> <mn>10</mn> </mrow> <mrow> <mo>-</mo> <mn>6</mn> </mrow> </msup> <mo>-</mo> <msup> <mrow> <mn>10</mn> </mrow> <mrow> <mo>-</mo> <mn>3</mn> </mrow> </msup> </mfenced> </math></EquationSource> </InlineEquation>. This study of WNFM shows momentous associations for real-time applications.</p>

Artificial intelligence analysis of nonlinear radiative and chemically reactive Williamson nanofluid flow with motile microorganisms

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发表日期：

2025年11月11日

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Imran Abbasi,
Zohaib Arshad,
S. AlFaify,
Zahoor Shah,
Waqar Azeem Khan,
Taseer Muhammad

摘要

By virtue of significant thermal properties, nanofluids have much importance in medical field, pharmaceutical arrangements, electric batteries, chemical engineering areas and industrial heating and cooling processes. This study explores the changing effects of three-dimensional (3D) flow of (WNFM). Due to shear thinning feature of WNFM, this plays a vital role in chemical industries, plastic industries, oil industries, biotechnology and graphic designing. Modeled arrangement of PDEs is transfigured to arrangement of ordinary differential equations (ODEs) via similarity transformation. System of ODEs is then coded into Mathematica software. Numerical dataset is obtained by applying ND-Solve technique. Numerical dataset is then transferred into MATLAB for graphical study. Obtained system of ODEs is numerically solved by classy Levenberg–Marquardt backpropagation scheme (LMBS) joined with neural networks (NNs) of artificial intelligence (AI). Results are gauged through performance graphs under NNs of AI in LMBS. Engagement of regression illustrations (RIs), mean-squared errors (MEs) training state analysis (TSA), and histogram analysis of errors (AHEs) is considered for accuracy and convergence of results. Along temperature, concentration, bioconvection, and velocity profiles, various parameters are analyzed including Lewis number, thermophoresis parameter, Prandtl number, magnetic parameter, parameter of temperature ratio, thermal Biot number, parameter of chemical reaction, and parameter of Brownian motion. The absolute error factor ranges in the bracket of $\left[{10}^{-6}-{10}^{-3}\right]$ $[10^{- 6} - 10^{- 3}]$ . This study of WNFM shows momentous associations for real-time applications.