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M.M. Kenisarin, et al. Journal of Energy Storage 27 (2020) 101082 in small numbers and therefore was not widely accessible to the re- search community. The book of G.A. Lane is recently reprinted. Other comprehensive reviews such as [18–21] also remained mostly unknown to researchers in the field. On the other hand, over the last 20 years, a great number of research studies were published in which it was con- cluded that the natural convection had a dominant role in the melting process. Interestingly, this dominant role of natural convection in melting processes was already established in classical works of Sparrow et al. [45] and Hale and Viskanta [46], which were published about 40 years ago. 3. Heat transfer during melting of PCM inside a spherical enclosure 3.1. Constrained melting Khodadadi and Zhang [47] were the first to perform the computa- tional and experimental study of buoyancy-driven convection on the constrained melting within a spherical enclosure. The physical model considers a spherical container of radius R, which houses a solid PCM (silicon) at temperature Ti lower then Tm. The phase change material is initially subcooled. For time t > 0, a constant temperature (To), which is greater than the melting temperature, was imposed on the surface of the sphere, i.e., To > Tm. To validate the computational findings, a set of melting experiments were conducted. Paraffin wax was used as the PCM with the melting point of 62–64 °C and Prandtl number of about 57. Spherical bulbs with outside diameters of 51.5, 78.1, 94.0 and 123 mm were used in experiments. The PCM with a starting tempera- ture of 60 °C was placed into the water bath with a temperature of 73 °C. The process of paraffin wax melting was photographed, and these are presented in Fig. 2. The parameter t* in this figure is the di- mensionless time (Fo•Ste). For instance, the actual time needed to melt the PCM to the state, shown at the dimensionless time t* = =0.0293, corresponds to 134 min. Analysis of taken photographs demonstrated that the dominant role of buoyancy-driven convection occurs starting at t* = =0.0164. The numerical study and visual observations of the constrained melting carried out in [45] were summarized by authors as follows: • The conduction mode of heat transfer is dominant at the early stages • of melting; Melting process is much faster at the top region of sphere, compared • to its bottom part; The Rayleigh number determines the magnitude of natural con- vection effect in the melting process to a greater extent than the • Stefan number; The Prandtl number also has a significant effect on the melting • process; The observed intensive melting process at the top region of the Fig. 1. Solidification of one-dimensional slab at the fusion temperature [44]. sHmL2 to = , 2k (T T ) sfo (1) where ρs is the density of solid phase, ks is the thermal conductivity, Hm is the heat of fusion. From this formula, it follows that the solidification time depends linearly on the volumetric heat of fusion (ρHm) of the PCM and squared value of the layer's thickness. The solidification time also inversely depends on the thermal conductivity and the difference be- tween the PCM's freezing temperature and HTF's temperature. Due to the constancy of melting heat, the solidification time criti- cally depends on such the physical property as thermal conductivity, the design parameter (the thickness of PCM layer), and the operational parameter as (Tf − To). These highlighted crucially important factors should be the subject of optimization in any LHSS. For low-temperature solar heating systems combined with the latent heat storage system, it critically important to provide the optimal differences between the HTF temperature and the PCM temperature (Tf−To) during the charge and discharge of the LHSS. Due to the significant variation of HTF tem- perature in solar collectors, the HTF maximum temperature at charging process is restricted by the efficiency of the solar collector. On the other hand, the HTF temperature at discharge process is restricted by the minimum permissible temperature of the HTF. During the melting process, heat transfer is as a result of the com- bination of thermal conduction and natural convection mechanisms. Research groups headed by Profs E. M. Sparrow and R. Viskanta at Minnesota and Purdue Universities respectively made a significant contribution to understanding the processes of melting and solidifica- tion. Thus, Viskanta [17] has made the fundamental review of works performed before 1983. Unfortunately, this review book was published Fig. 2. Instantaneous photographs of melting of wax inside a spherical bulb [47]. 3PDF Image | Journal of Energy Storage 27
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