In this paper we present a new mathematical model for Bingham-like materials in which the core behaves as a visco-elastic Maxwell fluid. We deduce the model in a general 3D framework, using a thermodynamical approach based on the theory of natural configurations. We apply the model to the case of a plane Poiseuille flow driven by a time-dependent pressure gradient. The mathematical formulation of the latter case turns out to be a free boundary problem in which a parabolic equation and a dissipative wave equation are coupled together.
A mathematical model for Bingham-like fluids with visco-elastic core / Lorenzo Fusi;Angiolo Farina. - In: ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK. - ISSN 0044-2275. - ELETTRONICO. - 55:(2004), pp. 826-847. [10.1007/s00033-004-3056-5]
A mathematical model for Bingham-like fluids with visco-elastic core
FUSI, LORENZO;FARINA, ANGIOLO
2004
Abstract
In this paper we present a new mathematical model for Bingham-like materials in which the core behaves as a visco-elastic Maxwell fluid. We deduce the model in a general 3D framework, using a thermodynamical approach based on the theory of natural configurations. We apply the model to the case of a plane Poiseuille flow driven by a time-dependent pressure gradient. The mathematical formulation of the latter case turns out to be a free boundary problem in which a parabolic equation and a dissipative wave equation are coupled together.
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