On Modeling Laminar Flow through Variable Permeability Transition Layer

A generalized model of the variable permeability in the transition layer is introduced in this work. This model can handle flows with small Darcy number, and might be of utility in controlling permeability amplifications. A method of solution of the resulting inhomogeneous generalized Airy’s equation is presented together with a computational procedure for the arising generalized Airy’s functions and the generalized Nield-Kuznetsov function of the first kind. A complete solution is then provided for the tri-layer flow problem that involves flow over a porous layer with an embedded transition layer.