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M.M. Kenisarin, et al. Journal of Energy Storage 27 (2020) 101082 Fig. 23. Unconstrained melting phase front Fig. 24. Liquid fraction versus Stefan number in unconstrained melting [48]. 35 °C, respectively. Melting occurs almost instantaneously for the sur- face temperatures of 40 and 45 °C. In the case of surface temperature of 35 °C, a 30 min delay before the start of melting was observed. A low surface temperature resulted in an opposite effect on the melting rate. Low surface temperatures decrease the creation of the centers of crys- tallization on the sphere wall and affect the heat transfer rate through the natural convection. It causes a significant slowdown in the melting rate. Veerappan et al. [70] studied the heat transfer during phase change of the PCM in a spherical enclosure as a combination of conduction and natural convection process. They developed the analytical correlations for evaluating the dimensionless position of the solid-liquid interface in melting and solidification processes. Particularly for melting, the fol- lowing correlation was suggested at 40 °C with an initial sub-cooling of 1 °C [48]. temperature difference (To−Tm), were the main factors affecting the melting rate. Koizumi et al. [73] used the enthalpy method for numerical simu- lations. They proposed a stream function, in which a solid sphere was moving in a stagnant viscid fluid for elucidation of the unconstrained melting process of a solid PCM in spherical capsule. In the analysis of the melting process, authors of [73] considered the effect of Stefan number (Ste) and capsule diameter (D). In the numerical simulations and experiments, the initial conditions were applied in the form of constant and uniform temperature at 25 °C with a sub-cooling of 3 °C, and the isothermal boundary conditions (58 °C, Ste = 0.27) were used. The experiment was performed in a transparent plastic tank, filled with water at 58 °C (Gr = =4 × 108). The spherical capsule was made of plastic with 2 mm thickness and with an outer diameter (D) of 100 mm. The solid PCM initially occupied 85% of the enclosed space. The PCM was placed in stagnant water at about 58 °C, which is 30 °C higher than the PCM melting temperature of 28.1 °C. The inner diameter of the sphere was 96 mm, and the internal volume of the capsule was 463 cm3. The melting process was monitored and recorded with the use of a video-camera. The PCM, used in the experiment, was nOctadecane. The obtained results are presented in Fig. 25. Archibold et al. [74] performed the comprehensive parametric in- vestigation of melting of sodium nitrate in an aluminum spherical container with a diameter of 10, 20, 30, and 40 mm. The numerical investigation was based on applying the finite-volume and enthalpy porosity technique for solving Navier-Stokes and energy equations. The results of the comprehensive study are illustrated in Fig. 26. As it can be seen, all curves practically merge into a single curve. Data obtained using the correlation (12) of Assis et al. [71] was used for the com- parison purpose. As it was noted previously, that correlation had been derived for the low-temperature PCM (RT-27) and produces melting times, which are not significantly shorter than the experiments. Fig. 25. Comparison of predicted results with experiments: a – variation of molten fraction with time; b – variation of the solid-liquid front with time in visual observations and numerical study [73]. (6+ 3 effs2 +2 effs3)(1 = SteFo eff)=6, (16) R2qv ; keff = 0.202 Ra0.228 ( L )0.252Pr0.029; where = R2qv ; k(To Tm) keff (To Tm) kl L reqv is equivalent radius of the melting solid; L = =R – reqv; s = =σ/2R is the dimensionless position of the interface. Assuming s = 1 and taking into account that SteFo is the dimensionless time τ, the time for eff reqv f=116. eff 6+ eff (17) For solidification, the transient position of the interface for β < 6.0 was expressed as complete melting can be estimated as SteFo=6(s 1)+6 6 1 tan1 + 5.3753 3ln(6 + s2) tan1 s 66 (18) The obtained correlation was verified using experimental data of Adref and Eames in [67]. The deviations were found to be within 20% for the melting process. It was shown that the diameter of sphere and 12PDF Image | Journal of Energy Storage 27
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