In the present study, a numerical model of a shell and tube Cascaded Latent Heat Thermal Energy Storage System (CLHTESS) with three phase change materials (PCMs) in series is developed. The CLHTESS refers to the storage device with multiple PCMs (PCM^a, PCM^b and PCM^c) used to enhance the effective heat transfer between the heat transfer fluid (HTF) and the PCMs. In this respect, paraffins (Rubitherm^TM (RT) series) are used as PCMs and air is used as the HTF, which flows through the copper tube. A 3D numerical study has been carried out using the finite element method to study discharge/solidification characteristics using the COMSOL Multiphysics tool. The present study is conducted to optimise the discharging rate of the CLHTESS model over the single-PCM (PCM^b) model by fixing parameters, namely thermal energy storage capacity, volume, heat transfer surface area and overall effective aspect ratio (length/diameter). A series of three PCMs having their volumetric melting enthalpy in arithmetic progression and symmetric volume ratios of PCM blocks are selected to meet the design parameters mentioned above. A parametric study is conducted on the resulting cascaded system to optimise the volume ratios of PCM blocks PCM^a, PCM^b and PCM^c to minimise the discharging time. The results show that a significant decrease in the discharging time is achieved by fixing the volumes in the ratio of 0.8:1:0.8 (PCM^a:PCM^b:PCM^c). It is observed that increasing the volume of PCMb in CLHTESS is found to reduce the discharging time significantly than the single PCM model. Circumferential/Annular fins with a non-uniform distribution are added to the PCM blocks based on the discharging times of individual blocks of the CLHTESS, such that the overall discharging time is reduced further.