<p>Techniques based on artificial intelligence have gained popularity recently as a means of solving challenges across a vast array of industries. The optimization of heat transfer systems and fluid flow design is directed by the measurement of irreversibility and inefficiency in thermodynamic processes through entropy generation in fluids. The purpose of this work is to use neural networking to explore the behavior of two-dimensional Magnetohydrodynamic flow of Reiner-Rivlin fluid with entropy generation under Soret and Dufour effects. The system of partial differential equations of the flow model has been modified into the system of ordinary differential equations by applying the appropriate parameters without dimensions. By using Adam numerical solver via ND-solve in Mathematica to solve ordinary differential equations for multiple situations and calculating the variance of the Reiner-Rivlin parameter, magnetic variable, radiation variable, chemical reaction, Soret number and Dufour number with five different cases. These solutions are utilized in MATLAB’s ntstool applications to generate the Levenberg–Marquardt back-propagation method-based trained neural network. The Reiner-Rivlin fluid model is solved with the help of the proposed algorithm using mean squared error, time-series response, gradient analysis, regression, and histogram studies. Their outcomes are presented in a tabular and graph format that highlights the efficiency of the suggested Levenberg–Marquardt back-propagation algorithm. The convergence rate for gradient is around <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10773_2025_6023_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="39" /> </InlineMediaObject> <EquationSource Format="TEX">${10}^{-08}$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mn>10</mn> </mrow> <mrow> <mo>-</mo> <mn>08</mn> </mrow> </msup> </math></EquationSource> </InlineEquation>, validating the 98–99% accuracy and reliability of the suggested Levenberg–Marquardt back-propagation technique. The steady temperature distribution affects the flow and thermal aspect of the modeled fluid which causes changes in the energy dissipation and fluid’s viscosity. Analysis indicates that increasing Brinkman number, magnetic field, radiation as well as diffusion parameters significantly enhance entropy generation through increased heat transfer and fluid irreversibility.</p>

Entropy Generation in Reiner-Rivlin Fluid Flow Under Soret and Dufour Impact: Neural Networks Applications

期刊论文
发表日期：

2025年6月2日

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Muhammad Shoaib,
Shafaq Naz,
Muhammad Asif Zahoor Raja,
Rabia Khanam,
Iftikhar Ahmad,
Kottakkaran Sooppy Nisar

摘要

Techniques based on artificial intelligence have gained popularity recently as a means of solving challenges across a vast array of industries. The optimization of heat transfer systems and fluid flow design is directed by the measurement of irreversibility and inefficiency in thermodynamic processes through entropy generation in fluids. The purpose of this work is to use neural networking to explore the behavior of two-dimensional Magnetohydrodynamic flow of Reiner-Rivlin fluid with entropy generation under Soret and Dufour effects. The system of partial differential equations of the flow model has been modified into the system of ordinary differential equations by applying the appropriate parameters without dimensions. By using Adam numerical solver via ND-solve in Mathematica to solve ordinary differential equations for multiple situations and calculating the variance of the Reiner-Rivlin parameter, magnetic variable, radiation variable, chemical reaction, Soret number and Dufour number with five different cases. These solutions are utilized in MATLAB’s ntstool applications to generate the Levenberg–Marquardt back-propagation method-based trained neural network. The Reiner-Rivlin fluid model is solved with the help of the proposed algorithm using mean squared error, time-series response, gradient analysis, regression, and histogram studies. Their outcomes are presented in a tabular and graph format that highlights the efficiency of the suggested Levenberg–Marquardt back-propagation algorithm. The convergence rate for gradient is around ${10}^{-08}$ $10^{- 08}$ , validating the 98–99% accuracy and reliability of the suggested Levenberg–Marquardt back-propagation technique. The steady temperature distribution affects the flow and thermal aspect of the modeled fluid which causes changes in the energy dissipation and fluid’s viscosity. Analysis indicates that increasing Brinkman number, magnetic field, radiation as well as diffusion parameters significantly enhance entropy generation through increased heat transfer and fluid irreversibility.