Homogenization of a non-homogeneous heat conducting fluid. (English) Zbl 1511.35276
A flow of nonhomogeneous heat conducting fluid is considered in a three dimensional perforated domain. Under the critical assumption on the holes: the diameter of the small holes proportional to the cube of their mutual distance, a homogenization result is proved in the limit of those quantities approaching \(0\). The limiting equation contains a friction term modeling the Brinckman law which depends on the viscosity and on the geometric structure of perforation.
Reviewer: Piotr Biler (Wrocław)
MSC:
| 35Q35 | PDEs in connection with fluid mechanics |
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
| 35B27 | Homogenization in context of PDEs; PDEs in media with periodic structure |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 76M50 | Homogenization applied to problems in fluid mechanics |
| 74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |
| 74M10 | Friction in solid mechanics |
Keywords:
Navier-Stokes equations; heat conducting fluid; perforated domain; homogenization; Brinckman lawReferences:
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