Internally finned tubes and annuli may be used to enhance the heat transfer characteristics of double-pipe heat exchangers. The geometry (shape, height, pitch) of the fin cross section is key to deciding the overall performance of enhanced systems. In this work, to understand the effects of fin truncation, we modeled internally finned annuli with triangular fins that were selectively truncated (base/tip/base and tip). For this purpose, a numerical model in Ansys Fluent was set up and good agreement was obtained against empirical data. Pipe length was fixed at 100″; the fin pitch and height were varied in a set range. All resulting cases were run under turbulent-flow conditions at a fixed Reynolds number. The thermal conductance and pressure drop were the metrics used to quantify performance. Obtained data revealed that triangular fins with truncated base outperform all other shapes by up to 35%, whereas doubly truncated triangular fins perform best at high values of the fin pitch. A more exhaustive investigation of results is presented toward the end.