The convection-to-radiation converter (CRC) made of porous ceramics has been proven to be an effective means in the enhancement of heat transfer in burners, combustors, industrial furnaces and high temperature plug flow systems. The paper proposes a novel application using this CRC technique in a partial bypass flow system for potential heat transfer enhancement. Hydrodynamically fully-developed and thermally developing laminar how is assumed in a circular duct which is fitted with a porous core to enhance both convective and radiative transfer from a high-temperature gaseous medium to a heat-absorbing wall. The Navier-Stokes and modified Darcy equations are applied, respectively, to the flow held in a gas layer and porous core region. The radiation held is modeled by a two-dimensional S-type integral equation of transfer for its accuracy and efficiency in the numerical calculations. The effects of heat transfer augmentation using a porous CRC are investigated numerically for various flow and thermal parameters. Numerical solutions which include velocity profiles and flow characteristics of the CRC system as well as isotherm patterns, parameterization of the heat fluxes, mean bulk temperature and Nusselt number distributions along the how direction are presented.