Heat transfer analysis of magnetohydrodynamic nanofluid flow in blade coating process using cascade forward neural networks with Levenberg-Marquardt Scheme

• Governing PDEs are transformed into ODEs using appropriate transformations and Lubrication Approximation Theory, then solved numerically via BVP Midrich method for velocity, temperature, concentration, and microorganism profiles. • Novel CFNN-LMA framework accurately predicts heat transfer characteristics of magnetohydrodynamic Sutterby nanofluid during blade coating process, demonstrating exceptional precision in Nusselt number estimation. • Comprehensive model validation using multiple performance metrics including MSE, RMSE, TIC, MAD, R 2 , and error autocorrelation confirms the robustness and predictive reliability of the CFNN-LMA approach. • Physical analysis reveals significant influences of coating thickness parameter, magnetic field, Brownian motion, Grashof number, and bioconvection parameter on flow, heat transfer, and concentration characteristics. • Hybrid AI-numerical methodology demonstrates practical relevance for industrial coating processes, providing efficient computational framework for optimizing non-Newtonian nanofluid applications in manufacturing and materials processing. Background: Nanofluids and non-Newtonian fluids (N-N-Fs) are widely used in the polymer and chemical processing industries, particularly in applications such as printing technology, extrusion and coating processes. The accurate prediction of nanofluids rheological properties is important for optimizing their performance in these industrial applications. This work introduces a novel method that combines Cascade Forward Neural Networks (CFNN) with the Levenberg-Marquardt Algorithm (LMA) and a numerical method to analyze the magnetohydrodynamic (MHD) flow of Sutterby nanofluid (S-N-F) for the blade coating process (BCP). Objective: This study examines heat transfer by utilizing CFNN-LMA for the MHD flow of S-N-F, through considering various relevant physical phenomena. Methodology: The suitable transformations are applied to convert the system of governing partial differential equations (PDEs) into ordinary differential equations (ODEs), which are then further simplified using Lubrication Approximation Theory (LAT). The numerical solutions to the coupled ODEs for temperature, velocity, nanoparticle concentration, motile organisms and skin friction are obtained over a range of physical parameters using the Boundary Value Problem (BVP) Midrich method. This methodology improves both accuracy and efficiency, as demonstrated through the graphs and tabular form. A reference dataset for CFNN-LMA is generated in Maple software for various parameters to analyze heat transfer. The obtained reference data is then used for training in MATLAB with a 70% training split and 15% each for validation and testing. Outcomes : The accuracy of the CFNN-LMA model is validated using several performance metrics, including mean square error (MSE), fitness curves, regression analysis, error autocorrelation, loss function, solution comparisons, Theil’s Inequality Coefficient (TIC), and correlation between input and error. The best validation performance is achieved at approximately 10 - 11 , with Mu and gradient values ranging from 10 - 08 to 10 - 10 . The error histogram shows a value around 10 - 07 . Furthermore, material parameters are observed to significantly influence the velocity, temperature, nanoparticle concentration profiles, motile organisms and skin friction coefficients. Originality/Value : To date, no existing research has investigated the effects of S-N-F flow during the BCP under the influence of an MHD and multiple other physical effects. This study presents a novel approach to understanding these complex interactions, contributing new insights to the field of BCP.