Clear understanding of the characteristics on convective heat transfer in simple-configuration double-pipe heat exchangers will add great value to design of heat exchangers. In this work, an important while less investigated problem, i.e., turbulent forced convective heat transfer inside novel double-pipe heat exchangers with flat inner pipes, was investigated through CFD. The numerical prediction was first validated with available data. Then, effects of inner pipe geometry on flow and heat transfer were investigated. It was mainly found that effects of inner pipe geometry on thermal characteristics heavily depend on the value of Repipe. For Repipe < 7000, using flat inner pipes with small aspect ratio is beneficial to overall heat transfer, thermal effectiveness, and performance index. About 2.9%, 2.7%, and 16.8% increases in overall convective heat transfer coefficient, thermal effectiveness, and performance index, respectively, were achieved for a flat inner pipe with aspect ratio of 0.37. However, for Repipe > 7000, circular inner pipe significantly outperforms than flat inner ones. These results imply that at low Reynolds numbers, utilization of flat inner pipes with small aspect ratio is preferred to performance improvement for double-pipe heat exchangers, while circular inner pipe is still the best choice at high Reynolds numbers.