Asymptotic behavior of a non-Newtonian flow in a thin domain with Navier law on a rough boundary
We consider a non-Newtonian flow in a thin domain of thickness $\varepsilon$. The flow is described by the 3D incompressible Navier-Stokes (Stokes) system with a nonlinear viscosity, being a power of the shear rate (power law) of flow index $p$. The bottom of the domain is irregular by the present o...
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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2015 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/162340 |
| Acceso en línea: | https://hdl.handle.net/11441/162340 https://doi.org/10.1016/j.na.2015.01.013 |
| Access Level: | acceso abierto |
| Palabra clave: | non-Newtonian flow thin fluid films rough boundary Navier condition adherence condition asymptotic behavior |
| Sumario: | We consider a non-Newtonian flow in a thin domain of thickness $\varepsilon$. The flow is described by the 3D incompressible Navier-Stokes (Stokes) system with a nonlinear viscosity, being a power of the shear rate (power law) of flow index $p$. The bottom of the domain is irregular by the present of slight roughness of amplitude $\varepsilon^\delta$ and period $\varepsilon^\beta$, satisfying the relation $1<\beta<\delta$. Assuming pure slip or partial slip with a friction coefficient $\varepsilon^{-\gamma}$, with $\gamma>0$, on the rough boundary, we consider the limit when domain thickness tends to zero and we obtain different models depending on the magnitude $\delta$ with respect to ${2p-1\over p}\beta-{p-1\over p}$, and the magnitude $\gamma$ with respect to ${1\over p-1}$. |
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