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M.M. Kenisarin, et al. Journal of Energy Storage 27 (2020) 101082 Fig. 26. Generalized results for the melting process (Ref. 13 in the Figure corresponds to [71]) [74]. Therefore, the correlation, obtained in the considered work and pre- sented in Eq. (15) for the liquid mass fraction, produces an accurate prediction of characteristics of the storage system, based on the de- ployment of the spherical container. Fig. 27. Variation in the temperature of the water tank, containing PCM spherical shell, as a time function [75]. Table 2 Variation of the Stefan number and the Liquid fraction with time for different heater powers [75]. Time (min) 0 10 20 30 40 50 60 70 80 90 100 Stefan number Liquid volume fraction (%) 690W 850W 950W LMF = 1 112 1 FoSte3Gr4 . 2.9 (19) 690 W 0.0000 0.0237 0.0488 0.0795 0.1078 0.1376 0.1649 0.1937 0.2210 0.2458 0.2729 850 W 0.0000 0.0405 0.0776 0.1168 0.1506 0.1856 0.2225 0.2553 0.2859 0.3193 – 950 W 0.0000 0.0293 0.0652 0.1056 0.1437 0.1779 0.2133 0.2511 0.2893 – – 0.00 0.00 2.14 2.65 2.71 4.18 5.33 13.79 17.78 29.89 26.28 48.60 48.59 66.22 67.83 81.07 81.08 90.86 91.07 99.76 99.70 100.00 0.00 2.72 3.48 13.69 29.73 50.76 70.74 88.05 99.61 100.00 100.00 The correlation (19) was valid for the range of parameters used in simulated cases: 0.047 < Ste < 0.1; 1.2 × 104 < Gr < 1 × 105; and 7.2 < Pr < 9.1. Rizan et al. [75] conducted an experimental study of n-octadecane melting inside a spherical shell immersed in a water tank. The spherical samples subjected to the power flux of 690, 850 and 950 W. About 643.6 cm3 of solid n-octadecane were housed in a Pyrex spherical flask with the outer diameter of 110 mm, 1.5 mm thickness and neck's length of 168 mm. The flask was placed into an acrylic tank and suspended using a support stand. The tank had external dimensions of 30 cm (L) × 30 cm (W) × 50 cm (H). The thickness of its walls was 10 mm. The spherical flask was immersed into the 37.8-liter water volume with the Risheng Electrical Air Pump SP-780, secured at the center of its base floor. The flask was exposed to upward airflow to regulate heat dis- tribution. The results of the experiments are presented in Fig. 27 and Table 2. The tabular data can be used for validation of the numerical modelling of the PCM melting heat transfer inside a spherical enclosure with constant heat flux applied. Hosseinizadeh et al. [76] carried out numerical investigations of unconstrained melting of paraffin wax RT-27, which was enhanced by adding nano-size particles of copper. The developed mathematical model was verified by comparison with the data of Assis et al. [71]. As can be seen from Fig. 28a, there is a good agreement between calcu- lated values and experimental data presented by Assis et al. [71]. The typical temporal variations in the liquid fraction are shown in Fig. 28b. The thermophysical properties of the nano-enhanced composition used in simulations. They could be confirm the assumed values of thermophysical properties. It was also assumed that both solid and li- quid phases were homogeneous and isotropic. This last assumption is difficult to justify due to considerable differences in densities of copper and paraffin wax. There are evidences that the viscosity of composi- tions, enhanced with nanoparticles, exceeds that of the pure PCM more than ten times. The trivial conclusion, made by the authors, was that their simulation results indicated an enhancement in the melting rate of nano-enhanced composition, compared to conventional RT27. In the next paper, Hosseinizadeh et al. [77] reported the results of the comprehensive numerical and experimental investigations on un- constrained melting of n-octadecane inside a spherical capsule. PCM melting observation was made in the spherical glass flask with a dia- meter of 101.66 mm. The experiments were carried out at three dif- ferent wall temperatures, namely 35, 40, and 45 °C, with a sub-cooling of 1 °C. Numerical simulations were performed using Fluent 6.3 soft- ware for different values of Stefan numbers and different capsule dia- meters (40, 60, 80, and 101.66 mm). The mushy zone constant to be employed in Fluent software was determined from their experimental results. A comparison of the current results with data of Assis et al. [71] is presented in Fig. 29a. As it can be seen, a good agreement between results is observed. Fig. 29 presents the generalized results for different Stefan numbers and shell diameters. The statistical analysis of 13PDF Image | Journal of Energy Storage 27
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