https://doi.org/10.1140/epjs/s11734-026-02376-x
Regular Article
Advanced data-driven thermal modeling of shear-rate-dependent nanofluid flow in blade coating process under slippage effects
1
Department of Mathematics, The Islamia University of Bahawalpur, Rahim Yar Khan Campus, 64200, Rahim Yar Khan, Pakistan
2
Department of Mathematics, The Islamia University of Bahawalpur, 63100, Bahawalpur, Pakistan
3
Department of Physics, College of Science, King Faisal University, PO Box 400, 31982, Al-Ahsa, Saudi Arabia
a
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b
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Received:
9
March
2026
Accepted:
6
May
2026
Published online:
19
May
2026
Abstract
This study presents heat transfer analysis of shear-rate-dependent non-Newtonian nanofluid during the blade coating process under blade slippage and magnetohydrodynamics (MHD). The current analysis employs Lubrication Approximation Theory (LAT) to reduce the governing non-linear fluid equations and to solve them with numerical simulation. Particular emphasis is placed on the thermal boundary layer behavior, heat transfer characteristics, and uniform coating thickness. The influence of Brownian motion and thermophoresis on temperature distribution and thermal transport performance is systematically investigated. To enhance predictive capability, the Bayesian regularization-based recurrent neural network (BR-ARNN) framework is implemented to approximate the numerical solutions. Statistical validation using mean squared error, regression metrics, and autocorrelation confirms high predictive accuracy with absolute errors of order 10⁻5, demonstrating its robustness in capturing heat transfer processes. Results indicate that the rheological Weissenberg number and nanoparticle diffusion parameters significantly influence the temperature profile by up to 9% and 14.5%, respectively. Coating thickness declines by up to 27% by involved parameters; controlling them may help influence the product’s performance, functionality, and durability. The present framework provides an efficient hybrid thermal and data-driven modeling approach applicable in advanced coating techniques and thermally sensitive industrial processes.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2026
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
