Mathematical derivation of a Reynolds equation for magneto-micropolar fluid flows through a thin domain
Résumé
In this paper we study the asymptotic behavior of the stationary 3D magneto-micropolar fluid flow through a thin domain, whose thickness is given by a parameter 0 < ε <1. Assuming that the magnetic Reynolds number is written in terms of the thickness ε, we prove that there exists a critical magnetic Reynolds number, namely Recm = ε^{ −2} , such that for every magnetic Reynolds number Rem with order smaller or equal than Recm, the magneto-micropolar fluid flow in the thin domain can be modeled asymptotically when ε tends to zero by a 2D Reynolds-like model, whose expression is also given.
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