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.