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M.M. Kenisarin, et al. Journal of Energy Storage 27 (2020) 101082 The combined effect of Bi and ε on solidification for Ste = =0.1 (Narasimhan Table 8 et al. [116]). Bi τ = =Fo for complete solidification % reduction in τ ε==0 ε = =0.1 ε = =0.3 8.50 2.69 1.92 1.72 1.7 ε = =0.1 2.88 4.31 13.93 19.24 19.30 ε = =0.3 20.93 31.72 41.81 45.74 46.20 0.1 10.75 1 3.94 5 3.30 100 3.17 500 3.16 Table 9 10.44 3.77 2.84 2.56 2.55 Fig. 45. Comparison of experiments and model predictions for solid fraction, V * as a function of FoSte for solidification of eicosane with xGnP volume frac- tions of 0%, 0.52%, 1.04% and 1.57% in water at Twater = =25 °C and in air at Tair = =25 oC and Uair = =25 m/s. The model prediction is based on Eq. (11) in the limit of Bi ? 1 for water cooling, and Eq. (11) at Uair = =25 m/s for air cooling. [113]. PCM. In experiments, three samples (pure TD, TD + +0.5 wt.% GNP, and TD + +1 wt.% NP) were tested. The results of measurements of thermophysical properties of samples are summarized in Table 7. Tests were carried out in a stainless-steel shell with the inner diameter of 57.6 mm and thickness of the wall equal to 1 mm. The spherical cap- sule, kept preliminarily for 5 hours at constant temperature of 38 °C, was quickly moved into the water tank, the temperature of which was set to be 5, 10, and 15 °C. The difference between the melting point and boundary temperature (ΔT =Tbath - Tm) was 32, 27 and 22 °C, respec- tively. The results of experiments are shown in Fig. 44. It can be seen in Fig. 44a that curves noticeably differ from each other. In Fig. 44b, the solidified fraction presented as a function of dimensionless time Fo and the curves for each boundary temperature are close to each other. No correlations for calculations were derived in this work. In their next study, Liu et al. [112] used the pure 1-tetradecanol as the PCM in experiments. They used the same experimental rig, which was employed in [111]. Experimental data obtained in [112] was in a good agreement with numerical data of Chandrasekaran et al. [109]. Considering that, the measured variations of solidification fraction were correlated to FoSte using the following polynomial equation with a high coefficient of determination equal to 0.9933: fs = 0.0382 + 3.32(FoSte)0.5 2.87(FoSte) (46) ε = =0 0.1 3.06 0.5 1.9 0.7 1.84 1.0 1.56 ε = =0.1 2.64 1.73 1.51 1.30 ε = =0.3 1.89 1.20 1.05 0.88 ε = =0.3 41.24 36.84 42.93 43.58 The combined effect of Ste and ε on solidification for Bi = =5 (Narasimhan et al. [112]). Ste τ = =Fo for complete solidification % reduction ε = =0.1 13.56 8.94 18.09 16.66 Fig. 47. Variations of the molten fraction as correlated to a combination of scaled dimensionless parameters (FoSte*) for all cases [117]. The regression analysis of data for the dimensionless heat transfer rate, i.e., Nu number as a function of FoSte produced the equation with an acceptable coefficient of determination of 0.9228: Nu = 3.23 exp[ 14.43(FoSte)] (47) The Eq. (47) is valid for 0.015 < FoSte < 0.24. Temirel et al. [113] carried out an experimental investigation of solidification of eicosane with and without nano additives inside a Fig. 46. Variation of solidified mass fraction with dimensionless time, obtained for pure PCM (water) and nano-PCM [115]. 24PDF Image | Journal of Energy Storage 27
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