Retrofitting heat exchangers with internally finned tubes and annuli is a popular method of enhancing their heat transfer characteristics. The most notable benefits include component miniaturisation and energy savings. Their implementation comes with an increase in pumping power; therefore, it is necessary to choose the design of fins prudently. Existing work has, for the most part, underutilised fins by implementing a small number of fins and/or making gaps between them. This work compares the performance of three different fin shapes in turbulent pipe flows, across a wide range of parameters. Numerical solutions obtained from Ansys Fluent are used in this parametric study. An exhaustive discussion is presented towards the end, detailing the effects of varying fin height and pitch, with reference to a plain pipe. The findings of our study demonstrate a clear trend where both thermal conductance and pressure drop increase with the height of the fins but decrease with an increase in the fin pitch. Moreover, towards the conclusion of our study, we provide a comprehensive comparison of various fin designs, which further contributes to our understanding of their relative performance.