Linear regression analysis of Williamson hybrid nanofluid flow with thermal radiation: Numerical simulation

Research Background: In the modern landscape of Industry 4.0 and technological advancements, the control of heat and fluid flow is critical in enhancing the performance and efficiency of industrial and energy systems. Hybrid nanofluids, due to their improved thermal conductivity and energy transport characteristics, have gained significant attention over conventional fluids. Issue: Despite their potential, the complex behaviour of hybrid nanofluids under the influence of magnetic fields, porous media, and thermal radiation remains insufficiently explored, especially for non-Newtonian models such as the Williamson fluid. A detailed understanding of these effects is essential for optimizing thermal systems. Method: This study investigates the Williamson hybrid nanofluid flow over a stretching sheet in a porous medium subjected to a magnetic field and thermal radiation. The governing nonlinear partial differential equations are converted into ordinary differential equations using similarity transformations and solved numerically using the Runge-Kutta-Fehlberg (RKF-45) method implemented in MAPLE-18. A regression model is also developed to predict skin friction and Nusselt number using key influencing parameters. Results: Convergence analysis demonstrates that the numerical solution remains stable and reliable within a relative tolerance range of 10 −6 to 10 −8 . A multiple linear regression model, developed using key parameters K , M , Rd , and Ec , shows excellent predictive performance with R 2 = 0.96127 for the skin friction coefficient and R 2 = 0.99905 for the Nusselt number. These findings validate the robustness of the regression model and highlight the critical influence of magnetic and radiative parameters on heat transfer behavior in hybrid nanofluid flow systems.