On the Solution of a Hyperbolic One-Dimensional Free Boundary Problem for a Maxwell Fluid

Autor: Lorenzo Fusi, Angiolo Farina
Jazyk: angličtina
Rok vydání: 2011
Předmět:
Zdroj: Advances in Mathematical Physics, Vol 2011 (2011)
Druh dokumentu: article
ISSN: 1687-9120
1687-9139
DOI: 10.1155/2011/606757
Popis: We study a hyperbolic (telegrapher's equation) free boundary problem describing the pressure-driven channel flow of a Bingham-type fluid whose constitutive model was derived in the work of Fusi and Farina (2011). The free boundary is the surface that separates the inner core (where the velocity is uniform) from the external layer where the fluid behaves as an upper convected Maxwell fluid. We present a procedure to obtain an explicit representation formula for the solution. We then exploit such a representation to write the free boundary equation in terms of the initial and boundary data only. We also perform an asymptotic expansion in terms of a parameter tied to the rheological properties of the Maxwell fluid. Explicit formulas of the solutions for the various order of approximation are provided.
Databáze: Directory of Open Access Journals
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