It is well-known that the effect of inertia on the free convection boundary layer flow induced by a uniformly heated horizontal surface in a porous medium is weak, and modifies the heat transfer characteristics at second-order. In this paper we consider the case where the inertia effects are sufficiently large that the leading-order boundary layer theory is modified; this is equivalent to reconsidering how sufficiently near to the leading edge that the induced velocities are large enough for inertia effects to arise, but sufficiently far from the leading edge that the boundary layer approximation remains valid : The resulting nonsimilar boundary layer equations are solved using the Keller-box method. Near the leading edge inertia effects are found to dominate, but Darcy-flow is re-established further downstream.