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<p>The growing demand for high-efficiency thermal management in engineering and industrial applications has made it essential to develop advanced nanofluid-based heat transfer mechanisms. However, optimizing heat and mass transfer in non-Newtonian fluids remains challenging due to their complex rheological behavior and thermal properties. This study employs artificial neural networks integrated with the Levenberg–Marquardt Algorithm (ANN-LMA) to analyze convective heat and mass transfer in Maxwell fluids containing tri-hybrid, hybrid, and mono-nanoparticle gels. The mathematical model is formulated based on conservation laws and the thermophysical interactions between the base fluid and nanoparticles. The governing equations are numerically solved using BVP4c method (with fast convergence), along with boundary layer approximations, to evaluate the influence of viscoelastic materials on velocity, temperature, and concentration distributions. Three different nanoparticle configurations are considered: tri-hybrid (MWCNTs, GO, MoS₂), hybrid (GO, MoS₂), and mono (MoS₂). A reference dataset for ANN-LMA training is generated using the bvp4c solver, covering a range of parametric variations and hypothetical cases. The model is validated through performance evaluations based on mean squared error (MSE), error distribution histograms, and regression analysis, ensuring high accuracy, stability, and predictive reliability. The results indicate that momentum relaxation time is a key factor in restoring lost momentum due to external disturbances. Additionally, fluids with higher viscoelasticity exhibit a reduced viscous region compared to those with lower viscoelasticity, as quantified by the Deborah number. An important observation is that as Deborah’s number increases, momentum transport declines significantly, particularly in tri-hybrid and hybrid nanofluid-based systems. This research provides a reliable computational framework for modeling and predicting heat transfer behavior in non-Newtonian nanofluids, which is critical for applications in cooling technologies, biomedical devices, and industrial thermal management. By utilizing ANN-LMA for intelligent prediction and optimization, the study offers a low-error, high-accuracy solution that enhances energy efficiency and system performance. The proposed model presents a cost-effective and scalable approach to improving thermal transport in advanced engineering applications, making it a valuable contribution to the development of smart thermal energy management solutions.</p>

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Thermal performance with neural network analysis of Maxwell fluid with hybrid and tri-nanoparticle interactions: a case study

  • 期刊论文

  • 发表日期：

    2026年4月21日

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  • Noreen Sher Akbar,
  • Tayyab Zamir,
  • Taseer Muhammad,
  • Muhammad Farooq,
  • Naeem Ullah,
  • Saira Shukat

摘要

The growing demand for high-efficiency thermal management in engineering and industrial applications has made it essential to develop advanced nanofluid-based heat transfer mechanisms. However, optimizing heat and mass transfer in non-Newtonian fluids remains challenging due to their complex rheological behavior and thermal properties. This study employs artificial neural networks integrated with the Levenberg–Marquardt Algorithm (ANN-LMA) to analyze convective heat and mass transfer in Maxwell fluids containing tri-hybrid, hybrid, and mono-nanoparticle gels. The mathematical model is formulated based on conservation laws and the thermophysical interactions between the base fluid and nanoparticles. The governing equations are numerically solved using BVP4c method (with fast convergence), along with boundary layer approximations, to evaluate the influence of viscoelastic materials on velocity, temperature, and concentration distributions. Three different nanoparticle configurations are considered: tri-hybrid (MWCNTs, GO, MoS₂), hybrid (GO, MoS₂), and mono (MoS₂). A reference dataset for ANN-LMA training is generated using the bvp4c solver, covering a range of parametric variations and hypothetical cases. The model is validated through performance evaluations based on mean squared error (MSE), error distribution histograms, and regression analysis, ensuring high accuracy, stability, and predictive reliability. The results indicate that momentum relaxation time is a key factor in restoring lost momentum due to external disturbances. Additionally, fluids with higher viscoelasticity exhibit a reduced viscous region compared to those with lower viscoelasticity, as quantified by the Deborah number. An important observation is that as Deborah’s number increases, momentum transport declines significantly, particularly in tri-hybrid and hybrid nanofluid-based systems. This research provides a reliable computational framework for modeling and predicting heat transfer behavior in non-Newtonian nanofluids, which is critical for applications in cooling technologies, biomedical devices, and industrial thermal management. By utilizing ANN-LMA for intelligent prediction and optimization, the study offers a low-error, high-accuracy solution that enhances energy efficiency and system performance. The proposed model presents a cost-effective and scalable approach to improving thermal transport in advanced engineering applications, making it a valuable contribution to the development of smart thermal energy management solutions.