Pressure filtration of the Newtonian fluid in the Darsi-Brinkman approximation through the horizontal porous rectangular channel with orthotropic anisotropy

Abstract

We propose a mathematical model of the pressure flow of a viscous incompressible fluid in a porous horizontal channel with a rectangular cross section having an anisotropic structure described by an orthotropic tensor. The motion of the Newtonian fluid was assumed to be laminar (internal Reynolds number Re<50) and inertialess, as well as unidirectional along the axial direction of the porous channel, which allowed us to use the Darcy-Brinkman phenomenological equation, for which we formulated an initial-boundary-value problem, the solution of which we obtained analytically using a one-sided integral Laplace transformation and the finite integral Fourier transformation. A comparative analysis with known experimental data showed the correctness of the physical linearization of the Darcy-Brinkman equations. We show that mathematically filtering in a porous isotropic and anisotropic layer is described identically. The difference is in the values of the Darcy numbers, which characterize the internal structure of the granular layers.