A numerical study is developed to examine the behavior of the forced/free convective flow towards a stretchable Riga plate with generalized Fourier’s law. The flow is saturated through Darcy–Forchheimer porous space and generated due to linear and second-order velocity slip phenomena. Here, the main consideration is given to the energy equation which is modeled in the presence of generalized Fourier’s law and heat generation absorption. Stagnation point is also discussed. Appropriate similarity variables lead to ordinary differential equations. The dimensionless coupled equations i.e., momentum and energy are numerically solved by the Built-in-Shooting method. The obtained results divulge that the velocity field declines versus rising values of Darcy–Forchheimer number. The temperature field of the working fluid boosts versus higher estimation of Eckert number and heat generation/absorption parameter. The important factors i.e., skin friction coefficient and temperature gradient of this research work are calculated by graphically subject to mixed convection parameter, modified Hartmann number, Prandtl number and heat generation parameter. It is observed from the graphical results that the impact of skin friction is more between the stretched Riga surface and fluid particles in the presence of rising values of mixed convection parameter.