On the Solution of a Hyperbolic One-Dimensional Free Boundary Problem for a Maxwell Fluid
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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2011-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2011/606757 |
| Summary: | 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. |
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| ISSN: | 1687-9120 1687-9139 |