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...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2011/606757 |
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| _version_ | 1832568521500917760 |
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| author | Lorenzo Fusi Angiolo Farina |
| author_facet | Lorenzo Fusi Angiolo Farina |
| author_sort | Lorenzo Fusi |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-b7732e5f388f470d84baa4ef843f0f9e |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-b7732e5f388f470d84baa4ef843f0f9e2025-02-03T00:58:53ZengWileyAdvances in Mathematical Physics1687-91201687-91392011-01-01201110.1155/2011/606757606757On the Solution of a Hyperbolic One-Dimensional Free Boundary Problem for a Maxwell FluidLorenzo Fusi0Angiolo Farina1Dipartimento di Matematica “Ulisse Dini”, Università degli Studi di Firenze, Viale Morgagni 67/A, 50134 Firenze, ItalyDipartimento di Matematica “Ulisse Dini”, Università degli Studi di Firenze, Viale Morgagni 67/A, 50134 Firenze, ItalyWe 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.http://dx.doi.org/10.1155/2011/606757 |
| spellingShingle | Lorenzo Fusi Angiolo Farina On the Solution of a Hyperbolic One-Dimensional Free Boundary Problem for a Maxwell Fluid Advances in Mathematical Physics |
| title | On the Solution of a Hyperbolic One-Dimensional Free Boundary Problem for a Maxwell Fluid |
| title_full | On the Solution of a Hyperbolic One-Dimensional Free Boundary Problem for a Maxwell Fluid |
| title_fullStr | On the Solution of a Hyperbolic One-Dimensional Free Boundary Problem for a Maxwell Fluid |
| title_full_unstemmed | On the Solution of a Hyperbolic One-Dimensional Free Boundary Problem for a Maxwell Fluid |
| title_short | On the Solution of a Hyperbolic One-Dimensional Free Boundary Problem for a Maxwell Fluid |
| title_sort | on the solution of a hyperbolic one dimensional free boundary problem for a maxwell fluid |
| url | http://dx.doi.org/10.1155/2011/606757 |
| work_keys_str_mv | AT lorenzofusi onthesolutionofahyperboliconedimensionalfreeboundaryproblemforamaxwellfluid AT angiolofarina onthesolutionofahyperboliconedimensionalfreeboundaryproblemforamaxwellfluid |