Abstract
The goal of this study is to provide analytical and numerical assessments to a fluid flow based on an Eyring-Powell viscosity term and a Darcy-Forchheimer law in a porous media. The analysis provides results about regularity, existence and uniqueness of solutions. Travelling wave solutions are explored, supported by the Geometric Perturbation Theory to build profiles in the proximity of the equation critical points. Finally, a numerical routine is provided as a baseline for the validity of the analytical approach presented for low Reynolds numbers typical in a porous medium.