Modeling of magnetohydrodynamic Casson nanofluid flow with nonlinear thermal radiation in a stretching porous channel using ANN and Levenberg–Marquardt optimization

Abstract

This study presents a computational approach to investigate the impact of nonlinear thermal radiation on the magnetohydrodynamic (MHD) flow of Casson nanofluids (Ag/H₂O and CuO/H₂O) over an expanding wall within a permeable path, considering heat generation/absorption and suction effects. The governing partial differential equations (PDEs) are transformed into nonlinear ordinary differential equations (ODEs) using a similarity transformation and are numerically solved via the Runge-Kutta method with the shooting technique. As a key novelty, an artificial neural network (ANN) model utilizing Levenberg-Marquardt (LM) optimization is developed to enhance predictive accuracy by integrating heat-related factors and the solid volume fraction. The graphical analysis of numerical results illustrates how key parameters influence velocity, temperature, skin friction and the Nusselt number. Comparisons with existing literature confirm the high accuracy of predicting skin friction coefficients and heat transfer rates. The ANN-LM model achieves R-values very close to one across all response variables, indicating strong model performance. Overall, the study results demonstrate that the developed ANN-LM model is highly accurate in predicting skin friction coefficients and the Nusselt number. The findings highlight the significant role of nonlinear thermal radiation in optimizing nanofluid-based cooling systems, with potential applications in biomedical engineering, electronics cooling and energy transport technologies.