Homogenization of a non-homogeneous heat conducting fluid

0546793 - MÚ 2022 RIV NL eng J - Journal Article
Feireisl, Eduard - Lu, Y. - Sun, Y.
Homogenization of a non-homogeneous heat conducting fluid.
Asymptotic Analysis. Roč. 125, 3-4 (2021), s. 327-346. ISSN 0921-7134. E-ISSN 1875-8576
EU Projects: European Commission(XE) 320078 - MATHEF
Institutional support: RVO:67985840
Keywords : non-homogeneous Navier–Stokes system * homogenization * heat-conducting fluid * incompressible fluid * Brinkman law
OECD category: Pure mathematics
Impact factor: 1.259, year: 2021
Method of publishing: Limited access
https://doi.org/10.3233/ASY-201658

We consider a non–homogeneous incompressible and heat conducting fluid confined to a 3D domain perforated by tiny holes. The ratio of the diameter of the holes and their mutual distance is critical, the former being equal to ε3, the latter proportional to ε, where ε is a small parameter. We identify the asymptotic limit for ε→0, in which the momentum equation contains a friction term of Brinkman type determined uniquely by the viscosity and geometric properties of the perforation. Besides the inhomogeneity of the fluid, we allow the viscosity and the heat conductivity coefficient to depend on the temperature, where the latter is determined via the Fourier law with homogenized (oscillatory) heat conductivity coefficient that is different for the fluid and the solid holes. To the best of our knowledge, this is the first result in the critical case for the inhomogenous heat–conducting fluid.
Permanent Link: http://hdl.handle.net/11104/0323171