Mathematical analysis for 3D Williamson nanofluid flow past a bi-directional stretched surface in Darcy-Forchheimer permeable media constitutes the focus of this study. The novelty of the proposed model is augmented by the addition of thermal and solutal stratification with chemical species and variable thermal conductivity. Calculations of the suggested model are conducted via the renowned homotopy analysis method (HAM). The results obtained are validated by comparing them in a limiting form with an already published article. Excellent harmony is achieved in this regard. Graphical structures, depicting impacts of assorted arising parameters versus the profiles involved are also provided. It is noticed that the velocity profile is a dwindling function of the Williamson parameter and Hartmann number. It is also stated that the Cattaneo-Christov heat flux exhibits conventional Fourier and Fick’s laws behavior when both coefficients of thermal and concentration relaxations are zero.