Magneto-thermal convective heat transfer and sensitivity analysis of Bingham–Papanastasiou fluid around an isothermal cylinder in trapezoidal enclosure

Purpose The purpose of this study is to investigate the interaction of a Bingham–Papanastasiou fluid with a heated circular cylinder inside an enclosure under magneto-thermal convection. The objectives are to analyze hydrodynamic phenomena, including entropy generation because of heat transfer and viscous dissipation, and to perform a relative sensitivity analysis to identify the most influential physical parameters affecting the average heat transfer rate at the heated cylinder. Design/methodology/approach The Navier–Stokes equations for Bingham–Papanastasiou fluid, coupled with the energy equation and viscous dissipation, are solved numerically using the finite element method in COMSOL Multiphysics 6.2. Relative sensitivity analysis of the average Nusselt number is carried out using response surface methodology (RSM) in MINITAB 21, using central composite design and analysis of variance (ANOVA). Findings The results of this study show that increasing the Rayleigh number enhances vortex size and streamline velocity. The Bingham–Papanastasiou dissipation has negligible impact on fluid circulation but causes a slight rise in fluid temperature while playing a key role in entropy generation within the enclosure. The RSM model for the average Nusselt number demonstrates high predictive accuracy, with an R2 of 99.57% and a predicted R2 of 98.78%. Local sensitivity analysis highlights the Rayleigh number as the most dominant parameter influencing the average Nusselt number and, consequently, the heat transfer rate. Originality/value This work provides new insights into magneto-thermal convection in Bingham–Papanastasiou fluids by combining finite element simulations with statistical sensitivity analysis. This study highlights the relative importance of governing parameters on heat transfer performance, particularly emphasizing the Rayleigh number’s role, which can guide future designs in thermal management and engineering applications involving non-Newtonian fluids.