Geodesic
Steady-state thermal Herschel-Bulkley flow with Tresca's friction law
Electronic journal of differential equations, Tome 2010 (2010)
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.
Classification : 35J85, 76D03, 80A20
Keywords: Herschel-Bulkley fluid, thermal friction law, variational inequality, weak solution 
@article{EJDE_2010__2010__a13,
     author = {Messelmi,  Farid and Merouani,  Boubakeur and Bouzeghaya,  Fouzia},
     title = {Steady-state thermal {Herschel-Bulkley} flow with {Tresca's} friction law},
     journal = {Electronic journal of differential equations},
     year = {2010},
     volume = {2010},
     zbl = {1190.35185},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a13/}
}
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%A Bouzeghaya,  Fouzia
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%J Electronic journal of differential equations
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%V 2010
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%F EJDE_2010__2010__a13
Messelmi,  Farid; Merouani,  Boubakeur; Bouzeghaya,  Fouzia. Steady-state thermal Herschel-Bulkley flow with Tresca's friction law. Electronic journal of differential equations, Tome 2010 (2010). http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a13/