Modeling couple stress effects in Oldroyd-b fluid flow over a wedge: A multiple linear regression and Bayesian neural network approach

This study investigates the steady, magnetohydrodynamic flow and heat transfer of an Oldroyd-B fluid over a wedge, incorporating the effects of thermal radiation, Joule heating, and couple stresses. The governing partial differential equations are reduced to a system of coupled ordinary differential equations through a set of suitable similarity transformations. The resulting nonlinear boundary value problem is solved numerically using the bvp4c solver in MATLAB, which employs a collocation scheme to achieve high-accuracy solutions. From the numerical data, predictive models for the skin friction coefficient and Nusselt number are developed via multiple linear regression, establishing quantitative relationships with key governing parameters. To ensure robustness and quantify predictive uncertainty, the regression outcomes are validated using a Bayesian neural network framework. The analysis demonstrates that increasing the couple stress parameter and magnetic field decelerates the flow, while the thermal radiation parameter and Eckert number significantly elevate the fluid temperature and entropy generation. The findings of this work have direct implications for optimizing thermal management systems, polymer processing flows, and the design of wedge-shaped components in aerospace and energy applications where viscoelastic fluid behavior and entropy minimization are critical.