Single-phase fluid flow through variable permeability porous layers is considered. The variable permeability layers are bounded by other porous layers of constant or variable permeability or bounded by free-space channels. This work is undertaken in order to shed further light on the characteristics of flow through layered porous media with variable permeability. To this end, Brinkman's equation and Darcy's law are cast in their more general forms that contain a variable permeability term. For the Brinkman equation, this translates into its reduction to a variable coefficient ordinary differential equation. The forms of the variable permeability function chosen result mainly in a reduction of Brinkman's equation to an Airy's inhomogeneous differential equation or a generalized Airy's inhomogeneous equation, which are analyzed and solved in this work. Other forms of variable permeability in Brinkman's equations have also been considered, together with various forms used in Darcy's law, and offer either an advantage in handling continuity at the interface between layers, or else they offer further insights in characteristics of the flow. When flow through a Darcy porous layer is considered, analysis shows that if the porous layer is infinite in depth, its permeability must essentially be constant.
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