Abstract
A flow of Eyring-Powell type constitutes a remarkable area of analysis to model non-Newtonian processes in fluids. The associated diffusion term comes from the general kinetic theory of liquids and permits to account for a wider diffusivity, which is applicable for qualitatively low to higher shear stresses. The goal of the present article is to introduce a generalization of an Eyring-Powell fluid by the introduction of a porous reaction term (of Darcy-Forchheimer type) and a perturbation with a higher order operator. In particular, we consider that our model is an extension of a classical Eyring-Powell fluid in the same manner as introduced for other equations (see the extended Fisher-Kolmogorov model). The obtained equation is novel and requires analysis about existence, regularity and uniqueness of solutions. Stationary solutions are explored under the definition of a Hamiltonian. In addition, profiles of solutions are obtained with an exponential scaling that ends in a Hamilton-Jacobi equation. Eventually, some numerical assessments are introduced to validate the hypothesis done, and to discuss about the accuracy of the analytical approach followed.