Homotopic fractional analysis of thin film flow of Oldroyd 6-Constant fluid

Abstract

The analysis of Oldroyd fluids; a class of Maxwell fluids which also bears Newtonian properties under some conditions, has important implications for different scientific and engineering/industrial applications. Examples of these fluids are typically dilute polymer solutions which demonstrate both viscous and elastic behaviors when subjected to strain. For unidirectional steady flows, the Oldroyd-B (3-Constant) model is the simplest when it comes to describing these behaviors. This model is not sufficient in certain cases, for instance, convergent flow channels, pulling effects, and other extensional flows. In all such scenarios, its application may lead to having out of bound tensile stresses. Hence, in all practicality, higher constants of the Oldroyd model are required to include different tensorial invariants. In this article, we perform this analysis in fractional space on Oldroyd fluids in thin-film flow context using the Oldroyd 6-Constant model for both lifting and drainage scenarios. Solutions to the highly non-linear fractional differential equations are obtained by means of the Homotopy Perturbation Method (HPM) along with fractional calculus. Validation and convergence of the solutions are confirmed by finding residual errors. To the best of our knowledge, the given problem has not been attempted before in fractional space. Various physical aspects, such as the velocity profile, volumetric flux and average velocities are determined and analyzed both graphically and in tabulation form as part of this analysis.

Keywords

• Oldroyd 6-Constant fluid
• Fractional differential equation
• Homotopy perturbation method
• Lifting and drainage
• Validity and convergence