This paper presents the numerical investigation of a PCM (Phase Change Material) based longitudinal fin heat sink. Paraffin RT44HC is used as a PCM. The fins and the base of the heat sink are made up of aluminum. Fins are taken as an integral part of the heat sink. Volume of fluid (VOF) model has been employed to simulate the melting behavior of the PCM. The temperature variation at the base of the heat sink, fin symmetry and PCM plane of symmetry are studied along with melt fraction and phase distribution contours. Then, the parametric study has been carried out by varying height of the fin, thickness of the fin, thickness of the base, number of fins and power input. It is observed that operational time strongly depend on number of fins, fin thickness, fin height and difference between critical temperature and melting temperature of PCM. Further, Taguchi method has been used to reduce the number of simulations in finding the best configuration with maximum operational time. By considering critical temperatures of 54.8 °C, 63 °C and 72.6 °C, the heat sink configuration with maximum operational time has been obtained.