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Annual Review of Heat Transfer, Vol. 15, p.131-177 https://doi.org/10.1615/AnnualRevHeatTransfer.2012004651 3.1.3. Anhydrous salts The cations are mainly alkali (e.g. Li, Na, K) and alkaline earth (e.g. Ca, Mg) metals. Anions which are considered include nitrates, nitrites, hydroxides, bromides, carbonates, chlorides, sulfates and fluorides. Many anhydrous salts are miscible and this results in a large variety of potential single salts and salt mixtures (binary and ternary systems). Table 7 shows selected examples of PCMs. For temperatures up to 350 °C, in particular alkali metal nitrates and nitrites and their mixtures are suitable PCMs, if requirements such as handling and steel compatibility are taken into account (Tamme 2008). 3.2. Heat transfer concepts Many metals, such tin or lead, are characterized by high costs and low melting enthalpy. Hence, metals are usually not considered as a PCM. A characteristic of the remaining candidate PCMs is a low thermal conductivity. Table 7 shows that the thermal conductivities of common PCMs are lower than 1 W/(mK). The thermal conductivity of the PCM affects significantly the power density and the heat transfer design of the system. The charge and discharge power of the storage system corresponds to the melting and solidification time of the PCM. Analytical solutions for the non-linear problems of melting and solidification date back to the 19th century. Analytical solutions of the melting and solidification are known only for a few special cases with simple geometries (e.g. plane wall, tube) (Yao 1989, Alexiades 1999). More complex geometries require numerical methods. As an analytical example, Equation 12 gives the solidification time of a PCM slab tw,s (plane wall). Important assumptions are that the liquid PCM is at the melting temperature Tm, the PCM is confined in a space of a finite thickness 0 < x < l, for times t > 0 the boundary surface at x = 0 is maintained at a constant temperature Tw below Tm. The only mode of heat transfer considered is heat conduction. Convection in the PCM melt is assumed to be absent. The quasistationary approximation is assumed. This means that the sensible heat can be neglected compared to the latent heat. Hence, small Stefan numbers St ≤ 0.1 are considered. For the PCM, isotropic and homogeneous material properties are assumed. Further assumptions are that the thermophysical properties are independent of temperature and that the PCM properties are equal in the solid and liquid phase. Hence, density differences and void formation are not included. A clearly defined solid-liquid interface due to melting of the PCM at a single temperature is assumed. The initial PCM temperature is the melting temperature in the liquid phase. Ls l2 tw,s 2s(Tm Tw) (12) An analytical solution for the solidification time of a PCM around a cooled tube without fins (hollow cylinder of PCM) is given by Baehr (Baehr 2006). Equation 13 defines this analytical solution as the product of the solution of the plane wall tw,s and the geometric cylinder factor CF (Equation 14). For this solution, the assumptions are the similar as discussed previously for the plane wall geometry. The PCM is confined in a space of a finite thickness R < x < R+l, for times t > 0 the boundary surface at x = R is maintained at a constant temperature Tw below Tm. The geometric cylinder factor CF depends solely on the dimensionless PCM thickness l/R (Equation 14). Figure 14 shows this function up to a maximum value of l/R = 100. Higher values are usually irrelevant for PCM-storage engineering.PDF Image | Annual Review of Heat Transfer
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