Assumptions

This section simplifies the original problem and helps in developing the theoretical models by filling in the missing information for the physical system. The assumptions refine the scope by providing more detail.

Thermal-Energy-Only: The only form of energy that is relevant for this problem is thermal energy. All other forms of energy, such as mechanical energy, are assumed to be negligible. (RefBy: TM:consThermE.)

Heat-Transfer-Coeffs-Constant: All heat transfer coefficients are constant over time. (RefBy: TM:nwtnCooling.)

Constant-Water-Temp-Across-Tank: The water in the tank is fully mixed, so the temperature of the water is the same throughout the entire tank. (RefBy: GD:rocTempSimp, IM:eBalanceOnWtr, and IM:eBalanceOnPCM.)

Temp-PCM-Constant-Across-Volume: The temperature of the phase change material is the same throughout the volume of PCM. (RefBy: GD:rocTempSimp, IM:eBalanceOnWtr, IM:eBalanceOnPCM, and LC:Uniform-Temperature-PCM.)

Density-Water-PCM-Constant-over-Volume: The density of water and density of PCM have no spatial variation; that is, they are each constant over their entire volume. (RefBy: GD:rocTempSimp.)

Specific-Heat-Energy-Constant-over-Volume: The specific heat capacity of water, specific heat capacity of PCM as a solid, and specific heat capacity of PCM as a liquid have no spatial variation; that is, they are each constant over their entire volume. (RefBy: GD:rocTempSimp.)

Newton-Law-Convective-Cooling-Coil-Water: Newton’s law of convective cooling applies between the heating coil and the water. (RefBy: GD:htFluxWaterFromCoil.)

Temp-Heating-Coil-Constant-over-Time: The temperature of the heating coil is constant over time. (RefBy: GD:htFluxWaterFromCoil and LC:Temperature-Coil-Variable-Over-Day.)

Temp-Heating-Coil-Constant-over-Length: The temperature of the heating coil does not vary along its length. (RefBy: IM:eBalanceOnWtr and LC:Temperature-Coil-Variable-Over-Length.)

Law-Convective-Cooling-Water-PCM: Newton’s law of convective cooling applies between the water and the PCM. (RefBy: GD:htFluxPCMFromWater.)

Charging-Tank-No-Temp-Discharge: The model only accounts for charging of the tank, not discharging. The temperature of the water and temperature of the phase change material can only increase, or remain constant; they do not decrease. This implies that the initial temperature A:Same-Initial-Temp-Water-PCM is less than (or equal) to the temperature of the heating coil. (RefBy: IM:eBalanceOnWtr and LC:Discharging-Tank.)

Same-Initial-Temp-Water-PCM: The initial temperature of the water and the PCM is the same. (RefBy: IM:eBalanceOnWtr, IM:eBalanceOnPCM, LC:Different-Initial-Temps-PCM-Water, and A:Charging-Tank-No-Temp-Discharge.)

PCM-Initially-Solid: The simulation will start with the PCM in a solid state. (RefBy: IM:heatEInPCM and IM:eBalanceOnPCM.)

Water-Always-Liquid: The operating temperature range of the system is such that the water is always in liquid state. That is, the temperature will not drop below the melting point temperature of water, or rise above its boiling point temperature. (RefBy: IM:eBalanceOnWtr, UC:Water-PCM-Fixed-States, and IM:heatEInWtr.)

Perfect-Insulation-Tank: The tank is perfectly insulated so that there is no heat loss from the tank. (RefBy: IM:eBalanceOnWtr and LC:Tank-Lose-Heat.)

No-Internal-Heat-Generation-By-Water-PCM: No internal heat is generated by either the water or the PCM; therefore, the volumetric heat generation per unit volume is zero. (RefBy: IM:eBalanceOnWtr, IM:eBalanceOnPCM, and UC:No-Internal-Heat-Generation.)

Volume-Change-Melting-PCM-Negligible: The volume change of the PCM due to melting is negligible. (RefBy: IM:eBalanceOnPCM.)

No-Gaseous-State-PCM: The PCM is either in a liquid state or a solid state but not a gaseous state. (RefBy: IM:heatEInPCM, IM:eBalanceOnPCM, UC:Water-PCM-Fixed-States, and UC:No-Gaseous-State.)

Atmospheric-Pressure-Tank: The pressure in the tank is atmospheric, so the melting point temperature and boiling point temperature are 0\({{}^{\circ}\text{C}}\) and 100\({{}^{\circ}\text{C}}\), respectively. (RefBy: IM:eBalanceOnWtr and IM:heatEInWtr.)

Volume-Coil-Negligible: When considering the volume of water in the tank, the volume of the heating coil is assumed to be negligible. (RefBy: DD:waterVolume_pcm.)