Artificial neural network estimation for heated convective Carreau nanofluid model under the influence of magnetic, heat source/sink and cross diffusions over an exponentially stretching sheet

This study provides a robust artificial neural network (ANN) framework for the predictive estimation of a heated convective Carreau nanofluid model (HCCNFM) affected by magnetic, heat generation/absorption, and cross-diffusion through an exponentially extending surface. The governing physical characteristics is described via a set of coupled, nonlinear partial differential equations (PDEs), that are deliberately reduced to a structure of ordinary differential equations (ODEs) via resemblance transformations to facilitate numerical modeling. The resulting boundary value problem has been addressed using the BVP4C technique in MATLAB program to get high-fidelity datasets which includes velocity, temperature, and concentration descriptions under different flow conditions and physical properties. These datasets are then used to train, validate, and test using multilayer feed-forward ANN architecture, designed with the Levenberg–Marquardt algorithm (LMA). The efficiency of the ANN model is meticulously assessed through multiple statistical metrics, such as mean square error (MSE), histogram errors (HE), regression plots, autocorrelation, and function fitting analysis. The prediction error is observed between 10−4 and 10−6 which confirm the accuracy of ANN-LMA model. It is observed that velocities of HCCNFM declines as the M increases while enhances for We1 and We2 for both shear-thinning and shear-thickening fluids. The HCCNFM temperature exhibits opposite trend for Q>0 and Q<0 for both shear-thinning and shear-thickening fluids. This hybrid numerical-ANN approach highlights significant potential for applications in thermal treatment, polymeric extrusion, and bioengineering mechanisms involving smart fluids.