In our previous works, it is clearly addressed that optimisation of fin profile is of vital importance in terms of the rate of heat transfer from a hot surface, and the optimisation procedure depends on several factors. Within the scope of this research, a longitudinal cylindrical fin profile is under interest for the optimisation research. The purpose is to investigate the effects of longitudinal parabolic perforations on the fin parameters such as temperature distribution, effectiveness and efficiency, in which the fin surface is cooled by natural convection and radiation. Different concavity levels are considered to form parabolic perforations. The rate of heat transfer from fin surface is numerically correlated with the fin mass with respect to different concavity levels. According to results, heat transfer from unit fin mass is enhanced with the new designs. The outcome of the study can be used to optimise the needs for particular applications by making a decision between heat loss and weight options. That is, the increase in the concavity level of the perforation results in a lighter and cheaper design, but yielding a lower heat loss. However, heat transfer from unit mass is still enhanced.