Optimization and sensitivity analysis of nanoparticle aggregation over separated stagnation point flow due to EMHD Riga plate using RSM and ANN

This study aims to determine the optimal circumstances for heat and momentum transport in a TiO₂/ethylene glycol nanofluid in an unsteady stagnation-point flow over an EMHD Riga plate, with a focus on nanoparticle aggregation. The originality of this study is in the concurrent integration of (i) aggregation and non-aggregation nanofluid models, (ii) Electromagnetic hydrodynamic (EMHD) actuation using a Riga plate under transient decelerating flow conditions, and (iii) a hybrid data-driven optimization framework integrating numerical modelling, artificial neural networks (ANN), and response surface methodology (RSM) for sensitivity and thermal optimization. The controlling partial differential equations are transformed into a system of ordinary differential equations by the application of appropriate similarity transformations. The MATLAB bvp4c solver solves the nonlinear ordinary differential system produced by the unstable boundary-layer equations. High-fidelity numerical data are used to train a Levenberg–Marquardt backpropagation artificial neural network (LMB-ANN) for precise prediction of velocity and temperature fields. RSM with a face-centered central composite design evaluates parameter sensitivity and optimizes the Nusselt number for both aggregation and non-aggregation cases, considering the unsteadiness parameter ( − 0.1 ≤ β ≤ − 1.0 ), the nanoparticle volume fraction ( 0.01 ≤ ϕ ≤ 0.04 ), and the thermal radiation parameter ( 0.2 ≤ Rd ≤ 1.0 ). Results show that increasing the negative unsteadiness parameter (stronger deceleration) drastically affects the flow structure, resulting in dual velocity profiles and a constant thermal boundary-layer thickness decrease. Nanoparticle aggregation increases effective viscosity, reducing velocities while improving thermal regulation. RSM study indicates that unsteadiness is the predominant component affecting heat transport, followed by thermal radiation and nanoparticle volume percentage. The quadratic regression models show high accuracy, with R² values over 99.9% for both aggregation phases. Aggregation improves thermal stability by making heat transport less susceptible to parameter changes, according to sensitivity studies. Advanced thermal management systems, micro-electromechanical devices, and energy conversion technologies can benefit from the integrated numerical–ANN–RSM framework's robust and efficient prediction, optimization, and control of EMHD nanofluid flows with aggregation effects.

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