In the present study, a numerical model of a vertical shell and tube latent heat storage system validated with the experimental data is presented. The developed model comprises of three blocks of phase change materials (PCMs) having melting point temperatures (T-m) 360 degrees C, 335.8 degrees C and 305.4 degrees C, respectively. A non-uniform distribution of fins in three PCM blocks is initially employed to study the performance of the single PCM system (T-m = 335.8 degrees C). The effect of inlet heat transfer fluid temperature on the charging and discharging performances of the single PCM and multiple PCM (m-PCM) systems is analysed by varying a Stefan number (Ste(ref)) parameter, calculated based on the single PCM system. The charging and discharging times for the m-PCM system are either similar or lesser than the single PCM system for Ste(ref) >= 1, however, there is an improvement of 21-25% in the specific power charged and discharged by the m-PCM system for all the Ste(ref) values (0.5, 1, 1.5 and 2) considered. By employing a compound enhancement technique which is a combination of non-uniform fin-distribution and PCM blocks length ratio optimization for the m-PCM system, 30% and 9% reduction in the charging and discharging time, respectively, over the single PCM system is achieved. (C) 2021 Elsevier Ltd. All rights reserved.