Analytical studies of Eyring-Powell fluid models

Abstract

PurposeWhen the literature is reviewed carefully, the analytical solutions of these types of models are missing. First using appropriate similarity transformation, the equations are reduced to dimensionless form (NODE). To solve the reduced models, ansatz-based methods are considered. Finally, the explicit form solutions are obtained and the effects of material parameters and Prandtl number on the velocity and temperature profiles are shown in figures by the exact solutions. This study aims to discuss the aforementioned solution.Design/methodology/approachOne of the non-Newtonian fluids is Eyring-Powell (EP) fluid which is derived from the kinetic theory of fluids. Two variations of EP model are considered to obtain the exact solutions that are missing in the literature. In order to obtain exact solutions, one of the ansatz-based methods is considered. The effects of material parameters and Prandtl number on the velocity and temperature profiles are shown in figures by the exact solutions. The results will guide to develop the model to predict the velocity profile and temperature profile when experimental data for dimensionless material parameters of EP fluid are available.FindingsFinally, the explicit form solutions are obtained and the effects of material parameters and Prandtl number are shown in the figures. The results will guide to develop of the model to predict the velocity profile and temperature profile when experimental data for dimensionless material parameters of EP fluid are available. For the modified EP models, only special cases are considered. The generalized form, i.e. the modified EP models, which include deformation parameters, will be considered in the authors' future work.Originality/valueWhen the literature is reviewed carefully, the analytical solutions of these types of models are missing so by this work, the gap in the literature is filled. The explicit form solutions are obtained and the effects of material parameters and Prandtl number on the velocity and temperature profiles are shown in figures.