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<p>This study presents an integrated computational fluid dynamics, machine learning surrogate modeling, and Pareto front identification (CFD-ML-Pareto) framework to analyze thermal performance and optimization methodology for an unsteady MHD nanofluid flow in a porous trapezoidal enclosure with a discrete sinusoidal heater, incorporating Darcy-Brinkman-Forchheimer porous resistance, Lorentz force, and Joule heating. The governing vorticity-stream function equations are solved by employing the finite-difference technique (FDM). A Multilayer Perceptron (MLP) neural network model is designed and trained by using the simulated CFD dataset to predict the average Nusselt number and maximum stream function. The results show excellent accuracy on the testing set with R<sup>2</sup>=0.9972&#xa0;for the average Nusselt number and R<sup>2</sup>=0.9912&#xa0;for the maximum stream function. The trained surrogate enables exhaustive evaluation of 576 discrete design combinations spanning the Rayleigh number (10<sup>3</sup>–10<sup>6</sup>), Hartmann number (0–50), Darcy number (10<sup>−4</sup>–10<sup>−2</sup>), nanoparticle volume fraction (0–0.06), and discrete heater length (0.2–0.8), while reducing computational time from hours to milliseconds. Findings show that increasing the Rayleigh number from 10<sup>3</sup> to 10<sup>6</sup>&#xa0;increases heat transfer by&#xa0;319%, and increasing the Darcy number from&#xa0;10<sup>−4</sup> to 10<sup>−2</sup> increases heat transfer by&#xa0;144%. The magnetic field suppresses flow circulation by&#xa0;22.1%&#xa0;when the Hartmann number increases from&#xa0;0 to 50.&#xa0;Pareto front analysis reveals a fundamental trade-off between thermal performance and energy efficiency. Correlation analysis ranks parameter influence as <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(Ra&gt;Da&gt; S&gt;\phi &gt;Ha\)</EquationSource> </InlineEquation> on heat transfer rate. The proposed CFD-ML-Pareto workflow provides a practical tool for engineers designing porous MHD thermal systems, enabling rapid performance prediction and identification of Pareto-optimal designs without exhaustive CFD simulations.</p>

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Thermal Transport Analysis and Pareto Front Identification Using a Machine Learning Surrogate Model in an Unsteady MHD-Driven Porous Trapezoidal Cavity

  • 期刊论文

  • 发表日期：

    2026年7月30日

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  • Rujda Parveen

摘要

This study presents an integrated computational fluid dynamics, machine learning surrogate modeling, and Pareto front identification (CFD-ML-Pareto) framework to analyze thermal performance and optimization methodology for an unsteady MHD nanofluid flow in a porous trapezoidal enclosure with a discrete sinusoidal heater, incorporating Darcy-Brinkman-Forchheimer porous resistance, Lorentz force, and Joule heating. The governing vorticity-stream function equations are solved by employing the finite-difference technique (FDM). A Multilayer Perceptron (MLP) neural network model is designed and trained by using the simulated CFD dataset to predict the average Nusselt number and maximum stream function. The results show excellent accuracy on the testing set with R2=0.9972 for the average Nusselt number and R2=0.9912 for the maximum stream function. The trained surrogate enables exhaustive evaluation of 576 discrete design combinations spanning the Rayleigh number (103–106), Hartmann number (0–50), Darcy number (10−4–10−2), nanoparticle volume fraction (0–0.06), and discrete heater length (0.2–0.8), while reducing computational time from hours to milliseconds. Findings show that increasing the Rayleigh number from 103 to 106 increases heat transfer by 319%, and increasing the Darcy number from 10−4 to 10−2 increases heat transfer by 144%. The magnetic field suppresses flow circulation by 22.1% when the Hartmann number increases from 0 to 50. Pareto front analysis reveals a fundamental trade-off between thermal performance and energy efficiency. Correlation analysis ranks parameter influence as \(Ra>Da> S>\phi >Ha\) on heat transfer rate. The proposed CFD-ML-Pareto workflow provides a practical tool for engineers designing porous MHD thermal systems, enabling rapid performance prediction and identification of Pareto-optimal designs without exhaustive CFD simulations.