<p>This study investigates the prevalence and temporal stability of dual solutions resulting from velocity slip and viscous dissipation on an unsteady Darcy-Forchheimer flow of Williamson nanofluid over a permeable shrinking surface with suction. The combined influence of chemical reactions, Joule heating, and magnetohydrodynamics are included as well in the study. With the assistance of similarity characteristics, the governing coupled equations get turned into a dimensionless set of non-linear ordinary differential expressions and numerically accomplished through the bvp4c built-in tool in MATLAB package. The outcomes are depicted through figures. The findings point out that two solutions prevail for the flow via a shrinking sheet given a specific values of sheet parameters. Interestingly, the stability analysis reveals that one of the solutions has positive lowest eigenvalues, which match the physical data and reliable. The graphical representation and mathematical explanation demonstrate how many novel characteristics impact the diverse boundary layer profiles, including Nusselt number, Sherwood number, and skin friction. As a result of their resistance to the flow, Darcy and Forchheimer porous media contribute significantly to the momentum boundary layer's diminishing thickness here. Here opposite tendencies detect with augmentation in Williamson fluid factor. For the first solution branch, the temperature pattern raises as the Eckert number gets higher, while it drops owing to the velocity slip factor. The concentration pattern diminishes as the reaction rate parameter and the Lewis number rise. The implemented approach for discovering dual solutions and studying stability examination is useful for fluid dynamics enthusiasts as it assists in identifying if a steady state solution is realistically meaningful. Streamlines are also drawn here.</p>