Pressure-driven flow of a rate-type fluid with stress threshold in an infinite channel |
| |
Authors: | Lorenzo Fusi Angiolo Farina |
| |
Affiliation: | Università degli Studi di Firenze, Dipartimento di Matematica “Ulisse Dini”, Viale Morgagni 67/A, I-50134 Firenze, Italy |
| |
Abstract: | In this paper we extend some of our previous works on continua with stress threshold. In particular here we propose a mathematical model for a continuum which behaves as a non-linear upper convected Maxwell fluid if the stress is above a certain threshold and as a Oldroyd-B type fluid if the stress is below such a threshold. We derive the constitutive equations for each phase exploiting the theory of natural configurations (introduced by Rajagopal and co-workers) and the criterion of the maximization of the rate of dissipation. We state the mathematical problem for a one-dimensional flow driven by a constant pressure gradient and study two peculiar cases in which the velocity of the inner part of the fluid is spatially homogeneous. |
| |
Keywords: | Implicit constitutive relations Natural configurations Rate-type fluids Free boundary problems |
本文献已被 ScienceDirect 等数据库收录! |