Electronic Journal of Differential Equations,
Vol. 2010(2010), No. 46, pp. 1-14.
Title: Steady-state thermal Herschel-Bulkley flow with Tresca's
friction law.
Authors: Farid Messelmi (Univ. Zian Achour de Djelfa, Algeria)
Boubakeur Merouani (Univ. Ferhat-Abbes de Setif, Algeria)
Fouzia Bouzeghaya (Univ. Ferhat-Abbes de Setif, Algeria)
Abstract:
We consider a mathematical model which describes the steady-state
flow of a Herschel-Bulkley fluid whose the consistency and
the yield limit depend on the temperature and with mixed boundary
conditions, including a frictional boundary condition.
We derive a weak formulation of the coupled system of motion and
energy equations which consists of a variational inequality for
the velocity field. We prove the existence of weak solutions.
In the asymptotic limit case of a high thermal conductivity,
the temperature becomes a constant solving an implicit total energy
equation involving the consistency function and the yield limit.
Submitted January 16, 2010. Published April 06, 2010.
Math Subject Classifications: 35J85, 76D03, 80A20.
Key Words: Herschel-Bulkley fluid; thermal friction law;
variational inequality; weak solution.