• Outlet air temperature and charge time are reduced with rising inlet air velocity. • PCM of high PCT is suitable for long period of work ACU and low PCT is suitable for short rush cooling load. • COP of the ACU in case of PCM 24 E is the greatest and PCM 29 Eu is the smallest. • PCM 26 E has the minimum CST and PCM 29 Eu has the longest CST at 0.96 m/s. • For constant mass, rising PCM plate length reduces charging time and saving power. A study on the thermal energy storage (TES) of phase change materials (PCM) coupled with the condenser of air conditioning unit (ACU) is carried out for PCM 24 E, PCM 26 E, and PCM 29 Eu. This coupling technique is based on using the cold energy storage (CES) of the PCM by the cold ambient air at night to cool the ACU condenser at daytime. The study is performed during charging and discharging of the CES at various inlet ambient air temperatures and velocities to the PCMs plates at day and night times. The mathematical model of the physical model is solved numerically by using ANSYS-Fluent software. The findings reveal that during the discharging process, the exit air temperature from the PCM plates is reduced with increasing the inlet air temperature and velocity. The coefficient of performant (COP) of the ACU coupled with the PCM is decreased with time. It starts by a higher value for low phase change temperature (PCT) than high PCT and after a period this trend is reversed. The time required to charge completely the PCM with CES for PCM 26 E is smaller than other studied PCMs at the same temperature difference between the PCT and the ambient. Decreasing the PCM plate width has the advantage of reducing the solidification time but it reduces the saving power by about 10.5%. The saving power due to using PCM rises with decreasing the ambient temperature and inlet air velocity. It is about 8.25, 8.4, and 8.95% for PCM 24 E, PCM 26 E, and PCM 29 Eu, respectively at ambient temperature 35 °C and air velocity 0.96 m/s. [ABSTRACT FROM AUTHOR]