Emden-Fowler Equation and Inverse Analysis of Simple Flows through Variable Permeability Porous Layers

Abstract

In this work we introduce an inverse method to analyze simple flows through variable permeability porous layers. Assuming that the velocity distribution is given, or specified as a function of the permeability, the governing equation is solved for the permeability distribution, then the velocity function is then recovered. Poiseuille-type flow involving Brinkman’s equation is considered together with other flow problems involving coupled parallel flow through composite layers. In case of flow through a Brinkman-Forchheimer layer over a Darcy layer, the governing equation was transformed into an Emden-Fowler equation whose solution provides a method for determining Beavers and Joseph slip parameter.