This paper presents numerical investigations on melting of phase change material using paraffin wax inside a double pipe heat exchanger. Numerical simulations are performed for melting of phase change material (PCM) in annulus while the inner pipe has two or four longitudinal fins and the results compared with inner bare tube. The aim of this study is to understand the PCM melting behaviors by observing the natural convection currents movement and melting fronts formation. It is concluded that melting performance of PCM can be significantly improved by applying longitudinal fins on the inner tube.