Conformable 1D steady-state Navier-Stokes equations to describe flow through porous media

Abstract

From the definition of a generalized conformable spatial derivative, an exponential conformable function with three parameters (a, b, α) is proposed for a viscous and an inertial-viscous steady-state Navier-Stokes 1D models, obtaining analytical solutions for both generalized conformable models. The conformable models' parameters are optimized to compare the viscous model to a Darcian 1D flow and the inertial-viscous model to a non-Darcian 1D model for a specific range of Darcy numbers (1 × 10 −2 < Da ≤ 1). Velocity profiles for the porous medium and the conformable model are computed and compared, showing that the generalized conformable Navier Stokes 1D models describe the flow through a porous medium, for both Darcian and non-Darcian flow, without including a Darcy term or macroscopic porous characteristics.