Heat transfer problems involving solid-liquid phase change are difficult to solve mainly because of the moving boundary that takes place between the solid and the liquid phase. The position of this boundary is not known, and must be determined as part of the solution, making phase change problems intrinsically nonlinear in nature. Although the moving boundary is the most significant problem, it is not the only one. Density changes in the PCM produce convective motion in the melt through natural convection, close-contact melting and volume changes. Complications also occur if there are subcooling/superheating effects, anisotropic phase change or phase change over an extended temperature range [32]. The model described in this document assumes that the heat transfer in the PCM is conduction dominated. From a mathematical point of view, buoyancy effects and the resulting natural convection motion in the liquid are tacitly ignored because they greatly complicate the analysis of predicting the interface position and heat transfer. From a physical point of view, this assumption is reasonable in order to avoid incongruent melting [32]. Analytical model In the configuration that we are modeling, the PCM is sandwiched between two concentric tubes of inner and outer radii ri and r0, The outside walls of the cylindrical capsule are adiabatic (see Figure 5-1) Heat transfer fluid is running through the inner pipe. Heat is conducted through the PCM and eventually melting (storage) or solidification (recovery) is triggered at the boundary x=ri. In order to reduce the computation time only one tube, only a single pipe with surrounding storage material is calculated. The energy stored by the system is then the product of the number
Heat transfer problems involving solid-liquid phase change are difficult to solve mainly because of the moving boundary that takes place between the solid and the liquid phase. The position of this boundary is not known, and must be determined as part of the solution, making phase change problems intrinsically nonlinear in nature. Although the moving boundary is the most significant problem, it is not the only one. Density changes in the PCM produce convective motion in the melt through natural convection, close-contact melting and volume changes. Complications also occur if there are subcooling/superheating effects, anisotropic phase change or phase change over an extended temperature range [32]. The model described in this document assumes that the heat transfer in the PCM is conduction dominated. From a mathematical point of view, buoyancy effects and the resulting natural convection motion in the liquid are tacitly ignored because they greatly complicate the analysis of predicting the interface position and heat transfer. From a physical point of view, this assumption is reasonable in order to avoid incongruent melting [32]. Analytical model In the configuration that we are modeling, the PCM is sandwiched between two concentric tubes of inner and outer radii ri and r0, The outside walls of the cylindrical capsule are adiabatic (see Figure 5-1) Heat transfer fluid is running through the inner pipe. Heat is conducted through the PCM and eventually melting (storage) or solidification (recovery) is triggered at the boundary x=ri. In order to reduce the computation time only one tube, only a single pipe with surrounding storage material is calculated. The energy stored by the system is then the product of the number