Due to the high enthalpy of fusion in water, ice storage systems are known as one of the best cold thermal energy storage systems. The phase change material used in these systems is water, thus it is inexpensive, accessible, and completely eco-friendly. However, despite the numerous advantages of these systems, the phase change process in them is time-consuming and this leads to difficulties in their practical application. To solve this problem, the addition of nanomaterials can be helpful. This study aims to investigate the compound heat transfer enhancement of a cylindrical-shaped unit equipped with double helically coiled coolant tubes using connecting plates and nano additives as heat transfer augmentation methods. Complex three-dimensional numerical simulations are carried out here to assess the best heat exchanger material as well as the impact of various nanoparticle types, including alumina, copper oxide, and titania, and their concentrations in the PCM side of the ice storage unit. The influence of these parameters is discussed on the charging rate and the temperature evolution factor in these systems. The results suggest that using nano additives, as well as the connecting plates, together is a promising way to enhance the solidification rate by up to 29.9%.