Waste thermal energy recovery from industrial exhaust gases is a popular way to reduce energy consumption for improving energy efficiency. Utilizing phase change materials (PCMs) is a promising approach. The PCM storage unit geometry is a key design factor, but less studied for the effect on PCM-based thermal energy storage enhancement. The study numerically investigates the PCM melting and thermal energy storage performances from the hot air in a square duct with different PCM storage configurations. Three types of PCM storage configurations that share the same PCM volume are considered: I-cuboid, II-concaved cuboid and III-convexed cuboid shapes. Variation of PCM storage geometry affects both air-PCM contact area and natural convection profiles in liquid PCMs during phase change. The three-dimensional transient simulations indicate that natural convection enhances PCM melting speed and thermal energy storage rate. The PCM storage configuration design angle shows remarkable impact during the PCM melting and affects the natural convection strength, PCM melting time, and heat storage rate. The convexed cuboid PCM storage configuration with a large angle at 133.8° presents the least melting time, reducing 24.9% of the melting time compared to the baseline cuboid configuration. This study might have potential to inspire more efficient PCM storage configuration designs for waste thermal energy recovery from industrial exhaust gases.