The increasing demand for higher energy efficiency in existing power generation facilities requires implementation of demand-side management strategies, such as valley filling and load shifting. As an operational strategy, thermal energy storage (TES) is considered as an effective means for shifting electric loads from on-peak to off-peak hours. For manufacturing storage tanks and design of systems, prediction of the time required for water solidification and accumulation of ice by numerical simulation and experimental methods is necessary. The objective of this study is to develop a numerical simulation model and determine the amount of time needed for solidification of water around a circular cross-section TES coil. To meet the objective, transient heat and mass transfer analysis of the water solidification phenomenon around a circular pipe with boundary and initial conditions similar to those found in ice TES systems is required. An extensive literature survey is made, and utilizing a finite difference algorithm suggested by Du-Fort Frankle, the cylindrical coordinate system based numerical model is developed and the time duration for solidification of 10 mm of ice around a 20 mm diameter pipe is found to be 2609.4 s.