A note on the Darcy-Forchheimer-Brinkman equation for fully developed flowthrough a porous channel bounded by flat plates

We consider the fully developed flow through straight porous channels, where the flow entry profiles are Poiseulle- Couette combinations. In particular, we use the Darcy-Forchheimer-Brinkman equation as the model governing the plane parallel flow through the porous medium. In the past, this particular model has been solved using numerical methods due to its nonlinear nature. We present an analytical solution of the problem employing an emerging perturbation technique, which has been proven to be successful in tackling nonlinear problems. We offer various verifications of the solution by comparing to existing, documented results and also mathematically, through reduction to simpler problems.