Comparative numerical and ANN investigation of heat transportation in mixed convective MHD Williamson nanofluid flow over a permeable wedge under the influence of viscous dissipation and suction.

This study presents a numerical and artificial intelligence-based investigation of two-dimensional, steady, mixed convective flow of a non-Newtonian Williamson nanofluid over an inclined wedge in the presence of viscous dissipation, magnetic field, suction, Brownian motion, and thermophoresis effects. The novelty of the present work lies in the combined consideration of these coupled transport mechanisms and the development of a Levenberg-Marquardt algorithm (LMA)-based artificial neural network (ANN) framework to predict the velocity, temperature, and concentration distributions from the numerical solutions. Such a combined Bvp4c-ANN approach provides an efficient alternative for predicting complex nonlinear nanofluid transport characteristics and enhances the applicability of the model to advanced thermal and industrial systems. The subsequent transformed equations are elucidated accurately using the MATLAB. Then, the generated numerical dataset is employed to train, validate, and test an ANN model using the LMA, with 70% of the data allocated for training and 15% each for validation and testing. The effects of pertinent convergence parameters on velocity, temperature, and concentration profiles are illustrated graphically and in tabular form. The results reveal that increasing the Williamson parameter suppresses the velocity field, whereas stronger viscous dissipation and thermophoresis enhance the thermal field. Brownian motion and thermophoresis significantly modify the temperature and concentration distributions through their coupled nanoparticle transport mechanisms. Moreover, increasing the Prandtl and Lewis numbers reduces thermal and concentration boundary-layer thicknesses, respectively. It is also observed that as the Biot number increases from (0.7 to 1.7), the Nusselt number increases by approximately 34.55%. The ANN results closely reproduce the numerical profiles with high regression coefficients and very small mean squared errors, confirming the robustness of the proposed predictive framework.