hal-03995934
https://hal.uca.fr/hal-03995934
https://hal.uca.fr/hal-03995934/document
https://hal.uca.fr/hal-03995934/file/AMIRAT.HAMDACHE.2023.pdf
doi:10.1016/j.jmaa.2023.127129
[PRES_CLERMONT] UniversitÃ© de Clermont
[CNRS] CNRS - Centre national de la recherche scientifique
[INSMI] CNRS-INSMI - INstitut des Sciences MathÃ©matiques et de leurs Interactions
[UMR6620] Laboratoire de Mathematiques
[ACL-SF] ACL en Sciences fondamentales
[TEST3-HALCNRS] TEST3-HALCNRS
Homogenization of ferrofluid flow models in porous media with Langevin magnetization law
Amirat, Youcef
Hamdache, Kamel
[MATH] Mathematics [math]
ART
Ferrofluid flow in porous media
Stokes equations
Langevin magnetization law
homogenization
two-scale convergence
Darcy law
The paper is concerned with the homogenization of the equations describing the flow of a ferrofluid through a heterogeneous porous medium $\Omega$ in the presence of an applied magnetic field. We discuss two models where the magnetization $M$ is parallel to the magnetic field $H$. In the first one $M$ and $H$ satisfy the relation$M=\lambda_0 \, {1}_{\Omega_f} H\, \mbox{ in } \Omega,$where $\lambda_0$ is a positive constant and ${1}_{\Omega_f}$ is the characteristic function of $\Omega_f$ (the pore space). In the second model, $M$ and $H$ satisfy the Langevin magnetization law$M= M_s \frac{L(b_1\, |H|)}{|H|} {1}_{\Omega_f} \, H,$where ${L}$ is the Langevin function given by $L(x)= \frac{1}{\tanh x} - \frac{1}{ x}$,$M_s$ is the saturation magnetization and $b_1$ is a positive physical constant.The velocity and the pressure satisfy the Stokes equation with a Kelvin magnetic force. We perform the homogenization of the equations of each of the two models. Using the two-scale convergence method, we rigorously derive the homogenized equation for the magnetic potential and determine the asymptotic limit of the magnetization. Then we rigorously derive a Darcy law.
2023
2023-08-17
en
http://creativecommons.org/licenses/by-nc-nd/
Journal of Mathematical Analysis and Applications
Elsevier