Optimising the thermal characteristics of Williamson fluid flow through a microchannel influenced by the Hall effect using response surface methodology

Response surface methodology plays a crucial role in optimising system performance by analysing the effects of key variables, such as channel dimensions and fluid flow conditions, to enhance heat transfer efficiency while minimizing pressure drops. This study focuses on the parametric optimization of Williamson fluid flow through a vertical, porous microchannel using response surface methodology, sensitivity analysis, and numerical simulations. The investigation incorporates the effects of the Hall current, non-linear thermal radiation, buoyancy forces, heat sources, convective heat transfer, and slip boundary conditions. The governing equations are solved numerically using the Runge-Kutta-Fehlberg method in conjunction with the shooting technique. The results reveal that increasing the magnetic parameter reduces entropy generation near the channel walls while increasing it within the flow region. The primary velocity diminishes, while the secondary velocity and thermal profile exhibit significant enhancements. Furthermore, an increase in the radiative parameter leads to higher entropy generation and Bejan number values, though the thermal profile declines with this parameter. Sensitivity analysis demonstrates that the magnetic parameter and Prandtl number exhibit positive sensitivity, while the temperature difference has a negative sensitivity. The squared coefficient is calculated to be 100 %, indicating excellent agreement between the predicted and observed values. These findings provide valuable insights into optimising the thermal and fluid characteristics of Williamson fluid flow in microchannel applications, with potential implications for advanced engineering systems.