In this paper, a comprehensive analysis of the second-order velocity slip phenomenon and stagnation point flow of cross nanofluid with a spectral relaxation approach over the geometry of porous medium is presented. Several other features are considered: mixed convection, passive control of nanoparticles, joules and viscous heating effect, thermophoresis, and Brownian motion. The velocity of the cross-nanofluid is judged by placing an inclined magnetic field. A set of partial differential equations (PDEs) are converted into ordinary differential equations (ODEs) using transform variables, and further ODEs are solved with the spectral relaxation approach, which is based on Gauss–Seidel relaxation method for computing numerical results. The numerical scheme using a physical quantity, the local Nusselt number, is made by quadratic multiple regression model and for the numerical solution of ODEs through Bvp4c. Comparison of the numerical values with quadratic multiple regression model and the Bvp4c technique is tabulated. This numerical outcome suggests that a large perturbation in the Nusselt Number is found when an increment in the thermophoretic parameter is given. Eckert number strengthens the thermophoretic and Brownian motion.