Analysis of Solutions, Asymptotic and Exact Profiles to an Eyring–Powell Fluid Modell

Abstract

The aim of this article was to provide analytical and numerical approaches to a one-dimensional Eyring–Powell flow. First of all, the regularity, existence, and uniqueness of the solutions were explored making use of a variational weak formulation. Then, the Eyring–Powell equation was transformed into the travelling wave domain, where analytical solutions were obtained supported by the geometric perturbation theory. Such analytical solutions were validated with a numerical exercise. The main finding reported is the existence of a particular travelling wave speed a=1.212 for which the analytical solution is close to the actual numerical solution with an accumulative error of 10−3.

Keywords

• travelling waves
• Eyring–Powell
• geometric perturbation
• nonlinear reaction–diffusion
• unsteady flow