Flow through and over a Brinkman porous layer of variable permeability, immersed in a fluid-filled channel, is modelled. The model governing equation through the porous layer inevitable gives rise to an inhomogeneous Weber's differential equation, solved in this work and solutions expressed in terms of parabolic cylindrical functions. Using state-of-the-art computational techniques and body of knowledge, the parabolic cylindrical functions are evaluated for a range of flow and medium parameters in order to illustrate intrinsic characteristics of the flow quantities. The approach followed in this work is novel and sets precedent in the study of flow through general porous media configurations and flow domains with variable permeability.

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