In the present paper, we analyzed the laminar boundary layer flow and heat transfer from a horizontal cylinder in a nanofluid-saturated non-Darcy porous medium in the presence of thermal radiation. This is the first paper presenting non-similar solutions for such a regime. The boundary layer conservation equations, which are parabolic in nature, are normalized into non-similar form and then solved computationally with an efficient, implicit, stable Keller-box finite-difference scheme. Non-Darcy effects are simulated via a second-order Forchheimer drag force term in the momentum boundary layer equation. The model used for the nanofluid incorporates the effects of Brownian motion, buoyancy ratio, and thermophoresis. A non-similarity solution is presented that depends on the Brownian motion number (Nb), buoyancy ratio (Nr), thermophoresis number (Nt), Forchheimer parameter (Λ), and radiation parameter (F). Velocity is reduced with increasing Forchheimer parameter, whereas temperature and nanoparticle concentration are both enhanced. The model finds applications in energy systems and thermal enhancement of industrial flow processes. © 2018 by Begell House, Inc.