Phase change materials (PCM) RT-28HC, RT-35HC, and RT-44HC with three different melting temperatures, 29 °C, 36 °C, and 44 °C, with similar thermal properties, are considered. The PCM is oriented from the left to right side of the heat sink in its increasing order. The fins are attached to the heat sink longitudinally, and its orientation effects are studied low (100–500 W/m²) and high (1000–5000 W/m²) heat fluxes applied on the horizontal bottom surface of the heat sink. A 2D model is developed using ANSYS Fluent 19, and the fin orientation effects are investigated numerically. The orientation of fins at different angles such as 0°, +15°, +30°, +45°, +60°,-15°,-30°,-45°, −60° are considered. The effect of fins on the charging cycle is assessed by comparing a single and double PCM heat sink. Three initial conditions are investigated by altering the initial temperature 300 K, 303 K, and 310 K. At increasing heat input, the negative angled fins possess a higher melting rate. For different initial conditions, −60° provides higher enhancement, and +60° possesses prolonged melting for almost all cases. The performance of a triple PCM design is compared with single and double PCM counterparts under similar conditions.