Deep Learning-Assisted Modelling of Electro-Osmotic Flow in Thin Film Sutterby Hybrid Nanofluid over a Porous Inclined Sheet

Irfan Saif Ud Din¹, Imran Siddique^2,3,4,5, Zohaib Zahid¹, Muhammad Nadeem⁶, Ibrahim Alraddadi^2,*, Taha Radwan^7,*
1 Department of Mathematics, University of Management and Technology, Lahore, Pakistan
2 Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah, Saudi Arabia
3 Department of Mathematics, University of Sargodha, Sargodha, Pakistan
4 Research Center of Astrophysics and Cosmology, Khazar University, 41 Mehseti Street, Baku, Azerbaijan
5 Jadara Research Center, Jadara University, Irbid, Jordan
6 Mechanical Engineering Department DAMEC, Postgraduate Program in Mechanical and Materials Engineering PPGEM, Research Center for Rheology and Non-Newtonian Fluids CERNN, Soft Matter Research Center SOFMAT, Federal University of Technology Parana UTFPR, Curitiba, PR, Brazil
7 Department of Management Information Systems, College of Business and Economics, Qassim University, Buraydah, Saudi Arabia
* Corresponding Author: Ibrahim Alraddadi. Email: email ; Taha Radwan. Email: email
(This article belongs to the Special Issue: Computational Advances in Nanofluids: Modelling, Simulations, and Applications)

Computer Modeling in Engineering & Sciences https://doi.org/10.32604/cmes.2026.081726

Received 13 March 2026; Accepted 20 April 2026; Published online 09 May 2026

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Abstract

This study examines the variable thermal conductivity and electroosmotic performance of Sutterby hybrid nanofluid (SBHNF) thin film flow over a stretched inclined sheet using an artificial neural network (ANN)-based on NARX (Multilayer Nonlinear Autoregressive Networks with Exogenous Inputs) multiple-layer backpropagation simulation with the Levenberg-Marquardt algorithm (LMA). AA7075 and AA7072 nanoparticles suspended in sodium alginate (SA) base fluid make up the hybrid nanofluid (HNF), which was selected due to its improved heat transfer properties and superior thermal conductivity. The model’s practical applicability is enhanced by melting heat, nonlinear thermal radiation, boundary slip, and Newtonian heating effects, which are considered for surface heat flow. A dataset spanning three cases and seven scenarios of SBHNF is generated by solving the simplified governing equations using the built-in MATLAB bvp4c numerical methods. The dataset comprises three divisions: 80% allocated for training, 10% for validation, and 10% for testing. The proposed system is employed for the analysis of stream and thermal transmission, with conclusions validated by several approaches, including error histograms, regression plots, time series analysis, mean square error (MSE) of the loss function, autocorrelation, and cross-correlation. Findings from the AI-based LMA validate the suggested method for solving the SBHNF accurately. Joule heating, variable thermal conductivity, and other external sources elevate fluid temperature, whereas radiation heating markedly amplifies surface heat energy by accumulating, hence improving heat transfer. The opposing forces produced by magnetic fields, Darcy’s law, and electro-osmosis reduce fluid velocity, which is effective for wellbore stability and hydraulic efficiency. The MSE and coefficient of determination (R²) are used to assess the correctness and robustness of the suggested computational framework. The trained network indicated outstanding predictive accuracy with R2=0.999 for all scenarios. The error histogram for the proposed model is 10−6 to 10−7. The seven scenarios of SBHNF fall within the range of 10−8 to 10−13 for the attained high MSE (loss function) convergence levels.