Darcy-Forchheimer Flow of Oldroyd-B Nanofluid Over an Inclined Plate with Exothermic Chemical Reactions and Bayesian Neural Network Modelling

This study investigates the steady, laminar motion of a non-Newtonian Oldroyd-B nanofluid over an inclined plate, integrating Buongiorno’s nanofluid model to account for Brownian motion and thermophoresis. The novel integration of couple stress and Forchheimer inertia in the analysis, coupled with advanced Bayesian-regularized ANN modelling, distinguishes this work. Governing equations are transformed using similarity variables and solved numerically via MATLAB’s bvp4c solver. The effects of couple stress, relaxation time, Forchheimer number, thermal radiation, thermophoresis, Brownian motion, and activation energy on velocity, temperature, and concentration profiles are systematically analyzed. Results reveal that couple stress and relaxation time reduce velocity, while thermal radiation and thermophoresis elevate temperature. Brownian motion decreases concentration, and activation energy influences both temperature and concentration oppositely. Multiple linear regression models quantify relationships between friction factor, Nusselt, and Sherwood numbers and key parameters, while a Bayesian-regularized artificial neural network (ANN) demonstrates high predictive accuracy (R-values ~1). It is noticed that increasing the couple stress parameter from 0.1 to 2.5 reduces friction factor by 59.8%, increasing the thermophoresis parameter from 0.1 to 2.5 decreases the Nusselt number by 7.8%, reflecting reduced heat transfer, and increasing the Brownian motion parameter from 0.1 to 2.5 reduces the mass transmission rate by 2.6%.