Lower-Dimensional Nonlinear Brinkman’s Law for Non-Newtonian Flows in a Thin Porous Medium

In this paper, we study the stationary incompressible power law fluid flow in a thin porous medium. The media under consideration is bounded perforated 3D domain confined between two parallel plates, where distance plates very small. perforation consists an array solid cylinders, which connect perpendicular direction, distributed periodically with diameters of small size compared to period. For specific choice thickness domain, found that homogenization Stokes system results lower-dimensional nonlinear Brinkman type law.