Heat and Mass Transfer in Bioconvective Carreau Nanofluid Flow Over Flat-Plate, Wedge and Stagnation-Point Geometries Using an Artificial Neural Network Approach

The present study investigates bioconvective Carreau nanofluid flow over flat-plate, wedge and stagnation-point geometries in the presence of magnetic porous resistance, thermal radiation and gyrotactic microorganisms. The governing nonlinear partial differential equations are transformed into a coupled system of ordinary differential equations by using similarity transformations based on the Falkner–Skan formulation. The transformed equations are then solved numerically by using MATLAB’s BVP4C solver and the generated numerical dataset is utilized to train an artificial neural network \(\:\left(ANN\right)\) using the Levenberg–Marquardt backpropagation algorithm. The \(\:ANN\) model is developed to predict the velocity, temperature, nanoparticle concentration and microorganism distributions for the considered flow configurations. The \(\:ANN\) approximations closely match the numerical solutions within the trained parameter ranges, with mean squared errors typically of order \(\:{10}^{-9}\) – \(\:{10}^{-10}\) . Validation and regression analyses confirm the stability and predictive capability of the proposed \(\:ANN\) framework. The comparative analysis further demonstrates that the flow geometry strongly influences the overall transport behavior, with stagnation-point flow exhibiting the highest sensitivity among the considered configurations. The results confirm that \(\:ANN\) based approaches can provide efficient approximations for nonlinear boundary-layer transport problems when trained using reliable numerical reference solutions.