Fractional Differential Models for Viscoelastic Fluids #

Ahlam Alghamdi

11:10 Monday in 4Q08.

Part of the Analysis of continuum mechanics session.

Abstract #

Fractional models can be used to describe viscoelastic behaviour such as stress relaxation under constant deformation, time-dependent deformation recovery followed by load removal, creep under continuous load, and time-dependent creep rupture. The problem of both steady and unsteady unidirectional flow of fractional viscoelastic fluids inside a real concentric cylinder rheometer (annular flow) is considered. A numerical method is developed for the solution of two coupled fractional differential equations (one for the velocity and the other for the stress), that appear in the pure tangential annular flow of fractional viscoelastic fluids. The spatial discretization is based on a spectral approximation. Numerical results have been presented that highlight the influence of the parameters in the fractional viscoelastic models on the numerical predictions.