Insight into the Eyring–Powell fluid flow model using degenerate operator: geometric perturbation

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This work provides a formulation of a fluid flow under a nonlinear diffusion based on a viscosity of Eyring–Powell type along with a degenerate semi-parabolic operator. The introduction of such a degenerate operator is significant as it allows us to explore a further general model not previously considered in the literature. Our aims are hence to provide analytical insights and numerical assessments to the mentioned flow model: firstly, some results are provided in connection with the regularity and uniqueness of weak solutions. The problem is converted into the travelling wave domain where solutions are obtained within an asymptotic expansion supported by the geometric perturbation theory. Finally, a numerical process is considered as the basis to ensure the validity of the analytical assessments presented. Such numerical process is performed for low Reynolds numbers given in classical porous media. As a main finding to highlight: we show that there exist exponential profiles of solutions for the velocity component. This result is not trivial for the non-linear viscosity terms considered.