Thermally simulated double diffusion flow for Prandtl nanofluid through Levenberg–Marquardt scheme with artificial neural networks with chemical reaction and heat transfer

The study explores the use of neural networks to analyze the behavior of Prandtl nanofluid near an extending surface, considering crude oil as the base fluid and copper nanoparticles. It examines the combined effects of thermal and concentration gradients on fluid flow and heat transfer characteristics through advanced computational techniques. The research focuses on double diffusion in the flow of Prandtl nanofluid near a stretching surface (DD-PNSS), utilizing the Levenberg–Marquardt scheme with artificial neural networks (LMS-ANNs). By applying similarity variables, the nonlinear partial differential equations are transformed into nonlinear ordinary differential equations. Through the application of the Lobatto IIIa formula in a three-stage process, various data sets are generated for the LMS-ANNs by varying parameters such as the Prandtl fluid parameter ( \(\alpha\) $\alpha$ ), Prandtl number (Pr), Brownian motion parameter (Nb), thermophoresis parameter (Nt), and Dufour-solutal Lewis number (Ld). The proposed LMS-ANNs model is meticulously tested, validated, and trained using a multi-stage approach, and its performance is compared to established references to ensure its reliability. The effectiveness of the suggested LMS-ANNs model is further affirmed through regression analysis, Mean Squared Error (MSE) evaluation, and histogram studies, showcasing an exceptional accuracy level ranging from \(1{0}^{-08}\) $10^{-08}$ to \(1{0}^{-10}\) $10^{-10}$ , setting it apart from alternative approaches and reference models. The study has application in optimizing heat and mass transfer processes. It is useful for catalytic reaction enhancement, energy transfer improvement in nanofluids, and efficient cooling system design. The growth of thermal management systems is supported by the incorporation of AI-driven algorithms, which provide accurate forecasts of heat and chemical transport phenomena under a variety of circumstances.