This work considers existing formulation of a recent problem introduced in the literature and involves flow through a transition porous layer, whose solution has been found in terms of Airy’s functions and evaluated using asymptotic series. Ascending series expressions are derived in this work and used in the computations of the solution, namely the computations of Airy’s functions and the recently introduced Nield-Kuznetsov function that arises in the solution to inhomogeneous Airy’s equation. Ascending series expressions developed in this work represent a viable methodology in analyzing flow through the variable permeability transition layer, and are shown to produce results as accurate as the asymptotic series results available in the literature. Both thin and fat transition layers are considered in this work which compares friction factors, velocity profiles, and mean velocities in the two types of layers, Flow through a channel over a Darcy porous layer is also considered in this work and the computed results agree with known results.