Galerkin weighted residual approach to the stability analysis of hydromagnetic hybrid nanofluid flow past a convective heating stretching/shrinking surface

Despite the importance of bifurcation analysis for controlling boundary layer separation and reducing drag force in aerodynamics and hydrodynamics, only a few mathematical methods have been explored in the literature. Remarkably, the Galerkin weighted residual method (GWRM) remains mostly unexplored in this regard. As such, the present study demonstrates the GWRM in the stability and bifurcation analysis of MHD hybrid nanofluid flow past a stretching/shrinking surface subjected to convective heating. The model governing equations are converted to ordinary differential equations (ODEs) via similarity variables. The GWRM is then modified to provide a solution and analyze the bifurcation and stability of the system. Some major findings indicate that a critical value [Formula: see text] exists for the shrinking parameter, below which there is no solution. Additionally, the presence of a magnetic field and suction terms enhances flow stability, indicating a delay in boundary layer separation, while the inclusion of hybrid nanoparticle terms hastens boundary layer separation. Furthermore, the suspension of [Formula: see text] nanoparticles in the fluid improves the heat transfer rate by 8.54% for the shrinking surface, 2.74% for the static surface, and 1.08% for the stretching surface, while the [Formula: see text] suspension improves heat transfer rate by 12.17% for the shrinking surface, 5.16% for the static surface, and 1.32% for the stretching surface. This indicates that geometric factors and the thermophysical properties of nanoparticles need to be considered in thermal management engineering. The findings in this study may assist in forecasting material stability, predicting failure mechanisms, and designing effective cooling systems for high-performance devices.