This study investigates the heat and flow characteristics of aggregating ternary-hybrid nanofluid by using stochastic machine learning method. Since much of the electricity generated is lost as heat during transportation, energy shortage has become a significant issue for industry in recent years. Minimizing the buildup of entropy during nanofluids flow and heat transmission is essential since heat transfer mechanisms are irreversible, thus the primary goal of this investigation is to investigate the consequences of heat radiation of nanoparticles aggregation and entropy formation on a viscous TiO2-C2H6O2nanofluids via a porous media surface that is exponentially permeable. The flow near the surface experience convective stagnation. The created PDE was transformed into an ODE, and the synthetic dataset generated is distributed in training (70%), testing (15%), and validation (15%). The stochastic (Levenberg–Marquardt) technique is used to verify the accuracy, validity, and efficiency of the artificial neural networks (ANNs) by testing with regression analysis, mean-squared error (MSE), error histograms, and evaluation relationship between numerical repetitions. The excellent performance of mean square error (MSE) achieved in the form of statistical values as 2.99E−10, 2.37 E−9, 3.23 E−9, 7.10 E−9, 6.43 E−09, 7.18 E−10, 2.53 E−09, 4.39 E−09 against 703, 341, 228, 812, 228, 583, 575 and 307 epochs for eight various scenarios. In this work it is observed that the increase in the Prandtl number, Mass transportation parameter, Eckert number and dynamic viscosity /density gives increase in the temperature profile <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14419_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="31" /> </InlineMediaObject> <EquationSource Format="TEX">$\theta (\eta )$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>θ</mi> <mo stretchy="false">(</mo> <mi>η</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> of the considered nanofluids aggregation model furthermore rising the values for the Eckert number, capacity for specific heat, as well as dynamic density /viscosity enhance the values of velocity profile <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14419_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="42" /> </InlineMediaObject> <EquationSource Format="TEX">$f{\prime}\left(\eta \right)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>f</mi> <mo>′</mo> <mfenced close=")" open="("> <mi>η</mi> </mfenced> </mrow> </math></EquationSource> </InlineEquation>, only increase in the value of Prandtl number gives the decline in the velocity profile <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14419_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="42" /> </InlineMediaObject> <EquationSource Format="TEX">$f{\prime}\left(\eta \right)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>f</mi> <mo>′</mo> <mfenced close=")" open="("> <mi>η</mi> </mfenced> </mrow> </math></EquationSource> </InlineEquation> .

Machine learning-based stochastic investigation of heat and momentum transfer in ternary-hybrid nanofluids with aggregation effects using artificial neural networks

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发表日期：

2025年7月21日

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Muhammad Zubair,
Hamid Qureshi,
Amer Hussain,
Waqar Azeem Khan,
Taseer Muhammad

摘要

This study investigates the heat and flow characteristics of aggregating ternary-hybrid nanofluid by using stochastic machine learning method. Since much of the electricity generated is lost as heat during transportation, energy shortage has become a significant issue for industry in recent years. Minimizing the buildup of entropy during nanofluids flow and heat transmission is essential since heat transfer mechanisms are irreversible, thus the primary goal of this investigation is to investigate the consequences of heat radiation of nanoparticles aggregation and entropy formation on a viscous TiO₂-C₂H₆O₂nanofluids via a porous media surface that is exponentially permeable. The flow near the surface experience convective stagnation. The created PDE was transformed into an ODE, and the synthetic dataset generated is distributed in training (70%), testing (15%), and validation (15%). The stochastic (Levenberg–Marquardt) technique is used to verify the accuracy, validity, and efficiency of the artificial neural networks (ANNs) by testing with regression analysis, mean-squared error (MSE), error histograms, and evaluation relationship between numerical repetitions. The excellent performance of mean square error (MSE) achieved in the form of statistical values as 2.99E⁻¹⁰, 2.37 E⁻⁹, 3.23 E⁻⁹, 7.10 E⁻⁹, 6.43 E⁻⁰⁹, 7.18 E⁻¹⁰, 2.53 E⁻⁰⁹, 4.39 E⁻⁰⁹ against 703, 341, 228, 812, 228, 583, 575 and 307 epochs for eight various scenarios. In this work it is observed that the increase in the Prandtl number, Mass transportation parameter, Eckert number and dynamic viscosity /density gives increase in the temperature profile $\theta (\eta )$ $θ (η)$ of the considered nanofluids aggregation model furthermore rising the values for the Eckert number, capacity for specific heat, as well as dynamic density /viscosity enhance the values of velocity profile $f{\prime}\left(\eta \right)$ $f' (η)$ , only increase in the value of Prandtl number gives the decline in the velocity profile $f{\prime}\left(\eta \right)$ $f' (η)$ .