Numerous theoretical and experimental studies were conducted on thermal energy storage utilizing phase change materials (PCMs). This study employs paraffin with particular properties as the PCM in a square solar water heater. Paraffin's melting point (MP) is 55 °C, the flow is transient, and natural convection is responsible for the heat transfer (HT). In this study, the effect of fin geometry, such as height (H) (3, 4, and 5 cm), and the number of fins (NoF) (double and triple), on the performance of the heat exchanger (HE) was investigated. For various parameters, temperature (T) and liquid fraction contours were produced. The results show that, the melting time (MT) for case A (without fins) about 3860 s. Based on the calculations, the reduction of MT for case B (with 3 fins) is 71%. The MT reduction at H=3, 4, and 5 cm equal to 48, 61, and 74% respectively.