This paper investigates combined laminar forced convection and radiation heat transfer of an absorbing-emitting gas in the entrance region of an elliptic duct with internal fins. The fins are continuous and longitudinal with zero thickness. The thermal conditions imposed on the elliptic duct are uniform temperature, both axially and peripherally. The method of moments, which models radiation in a partial differential equation, is employed to consider the radiation contribution. The three-dimensional energy equation and two-dimensional irradiation equation are diseretized and numerically solved by the control-volume based finite-difference method in the boundary-fitted coordinate system. The effects of six major parameters on the thermal behavior in the entrance region of the elliptic duct is discussed. These parameters are radiation-conduction, optical thickness, wall emissivity, Picltt number, fin height, and the minor axis to major axis ratio of the elliptic duct. The total Nusselt number variations show that heat transfer is enhanced by both thermal radiation and juts. Furthermore, the results are compared with the available data in the literature for pure forced convection with fins. We prove that radiation plays a significant role in the enhancement of heat transfer.