Abstract
In this work, the three-dimensional model for the compressible micropolar fluid flow is considered, whereby it is assumed that the fluid is viscous, perfect, and heat conducting. The flow between two coaxial thermoinsulated cylinders, which leads to a cylindrically symmetric model with homogeneous boundary data for velocity, microrotation, and heat flux, is analyzed.The corresponding PDE system is formulated in the Lagrangian setting, and it is proven that this system has a generalized solution locally in time.
Highlights
In this paper, we analyze the compressible flow of an isotropic, viscous, and heatconducting micropolar fluid, whereby we consider the flow between two coaxial thermoinsulated solid cylinders
The micropolar fluid is a type of fluid which exhibits microrotational effects, as well as microrotational inertia, and it can be perceived as a collection of rigid particles suspended in a viscous medium, which can rotate about the centroid of the volume element
The micropolar fluid was introduced by Eringen as an extension of the Navier–Stokes model, capable of treating phenomena at the microlevel
Summary
We analyze the compressible flow of an isotropic, viscous, and heatconducting micropolar fluid, whereby we consider the flow between two coaxial thermoinsulated solid cylinders. As we have already pointed out, we shall find a local generalized solution to problem (1)–(13) as a limit of approximate solutions ρn, vrn, vφn, vzn, ωrn, ωφn, ωzn, θ n , n ∈ N, (42) Where ρn, vrn, vφn, vzn, ωrn, ωφn, ωzn, and θ n are the approximations of the functions ρ, vr, vφ, vz, ωr, ωφ , ωz, and θ , respectively.
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