Farid Messelmi, Boubakeur Merouani, Fouzia Bouzeghaya
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 6, 2010.
Math Subject Classifications: 35J85, 76D03, 80A20.
Key Words: Herschel-Bulkley fluid; thermal friction law;
variational inequality; weak solution.
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Farid Messelmi Department de Mathematiques Univerisite Zian Achour de Djelfa Djelfa 17000, Algeria email: foudimath@yahoo.fr |
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Boubakeur Merouani Department de Mathematiques Universite Ferhat-Abbes de Setif Setif 19000, Algeria email: mermathsb@hotmail.fr |
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Fouzia Bouzeghaya Department de Mathematiques Universite Ferhat-Abbes de Setif Setif 19000, Algeria email: bouzeghaya@yahoo.fr |
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