The coupling of parallel flow, in a three-layer channel, with the main fluid flow sandwiched between two Darcy–Forchheimer–Brinkman (DFB) permeable layers of varying porousness is investigated in this work. A single binary model is proposed to characterize the flow through the channel. Within the transition porous layers, the reciprocal of the permeability is represented by a polynomial of degree n. Due to the lack of an analytical framework in this regard, cutting-edge computational tools are used to provide a novel insight into fluid dynamics in heterogeneous porous media (HPM). In this context, a solver capable of simulating heterogeneous porous media is created by modifying an open source software package openfoam's steady-state finite volume solver. The solver has first been checked and approved for the case of homogeneous porous media using the homotopy analysis method (HAM) and numerical data from previous literature. Then, a parametric study is conducted to identify the effect of a specific set of medium variables on flow characteristics and transport efficiency. The variables that can be changed include the Darcy number, permeability degree, free-space layer thickness, Reynolds number, and pressure gradient.