## 1 Introduction  
The enormous consumption of energy, especially for electrical demand from polluting energy sources, is expected to increase by 48% till 2040 [1]. There is then a growing interest in sustainable energy sources for the energy demand growth of power industries [2]. Thermal energy storage is an efficient method to shift the peak demand and to balance the electricity consumption [3]. Cold storage systems can shift the load from peak to off-peak hours. Cold storage during the low load periods can reduce the size of the system and decrease electricity needs. Additionally, it drastically reduces the cost of energy [4]. Using a thermal energy storage (TES) system in heating, ventilation, and air-conditioning (HVAC) systems can easily reduce energy costs and play a significant role in reducing carbon emissions [5]. In the case of intermittent energy sources such as solar systems, TES systems can be efficient to absorb and release energy during daylight and nighttime (heating purposes), respectively [6]. Cold storage technologies consist of the storage medium (liquid water, ice or eutectic salts among other examples) and the charge/discharge modes. Ice-on-coil storage (IOCS) devices consider either melting from the inside (internal melt) or outside (external melt) of a tube [7]. The charging process (solidification) is considered for these ice-on-coil ice storage systems. Cold heat transfer fluid, such as ethylene glycol, flows in the coil, and then ice is produced around the coil tube. The difference between these two types of ice storage systems is the melting process. In recent years, many experimental and numerical studies have been conducted to determine the performance of the ice storage system in HVAC systems. [PERSON] et al. [8] proposed different ways to decrease the power consumption of ventilation systems during peak hours using a comparative exergetic, economic and environmental analysis. It consisted of the addition of either an ice storage system or a phase-change material (PCM) to the HVAC system. Energy consumption for cooling purposes was found to be 4.9% and 7.5% lower than the one of conventional air conditioning systems, when one includes ice and PCM, respectively. It reduced also CO\({}_{2}\) emissions by 17.8% and 27.2%, respectively. [PERSON] et al. [7] reported that using ice storage significantly decreases the electricity demand during peak hours and so reduces the associated costs. There are also some investigations on the charge or discharge processes (melting and solidification) in ice storage systems. [PERSON] and [PERSON] [9] proposed to include either thin rings or fins to improve their ice-on-coil system. They revealed that the ice formation was improved by up to 34% and 21% using rings and fins, respectively. [PERSON] and [PERSON] [10] simulated freezing in a tank, with a specific volume around cylinders considering several arrangements. The combined influences of the number (between two and eight) and the arrangement of the cylinders were investigated. They reported the significant influence of the heat transfer between the cylinder walls and the surroundings in the four-cylinder configuration. [PERSON] et al. [11] studied the influence of the refrigerant inlet temperature on the ice formation in an IOCS system. The low inlet temperature of the refrigerant increases the thickness of the ice layer and the heat exchange efficiency. It has been confirmed by [PERSON] and [PERSON] [12] for ethylene glycol as refrigerant and by [PERSON] et al. [13]. These authors performed a combined energy and exergy analysis for an IOCS system. Reducing the refrigerant inlet temperature, from \(-5\) to \(-15\)\({}^{\circ}\)C, diminishes the storage charging time by a factor 2. For a vertical IOCS, [PERSON] et al. [14] examined the charging and discharging processes via a new efficient numerical approach based on the enthalpy method, named the sample and interpolation (SI) method. The proposed method was validated against experimental results for both charging and discharging processes.