Flow through Variable Permeability Composite Porous Layers

Flow through a variable permeability Brinkman porous layer with quadratic permeability function, underlain by a Darcy porous layer of variable linear permeability function is analysed. The model flow demonstrates the compatibility between the low-order Darcy law and the Brinkman equation in the sense that at the interface between the layers it is possible to impose equality of the non-zero shear stresses. A matching procedure is also introduced for velocity computation near the point of singularity associated with the resulting Cauchy-Euler equation.