Integral-Balance Solution to the Stokes' First Problem of a Viscoelastic Generalized Second Grade Fluid

TL;DR

This paper develops an integral-balance analytical solution for the Stokes' first problem in a viscoelastic generalized second grade fluid, highlighting the influence of fluid properties and parameters like the Deborah number on flow behavior.

Contribution

It introduces a novel integral-balance approach with an optimization-based parabolic profile for analyzing viscoelastic fluid flow in the Stokes' first problem.

Findings

The solution explicitly defines similarity variables related to viscous and elastic responses.

Numerical simulations show how parameters like Deborah number affect flow characteristics.

The method provides a closed-form solution adaptable to various flow conditions.

Abstract

Integral balance solution employing entire domain approximation and the penetration dept concept to the Stokes' first problem of a viscoelastic generalized second grade fluid has been developed. The solution has been performed by a parabolic profile with an unspecified exponent allowing optimization through minimization of the norm over the domain of the penetration depth. The closed form solution explicitly defines two dimensionless similarity variables and, responsible for the viscous and the elastic responses of the fluid to the step jump at the boundary. The solution was developed with three forms of the governing equation through its two dimensional forms (the main solution and example 1) and the dimensionless version showing various sides of the flow field and how the dimensionless groups control it: mainly the effect of the Deborah number. Numerical simulations demonstrating the effect of the various operating parameter and fluid properties on the developed flow filed have been performed.