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M.M. Kenisarin, et al. Journal of Energy Storage 27 (2020) 101082 34 Table 13 (continued) 123456 8 Shih and Chou [87] Pedroso and Domoto Analitic- NA NA Constant wall al temperature iteration method The formulas for analytical calculation of the solidification time versus dimensionless parameters The use of formulas give the results that sufficiently differ from numerical results [88, 89] Riley [90] A NA NA Constant wall temperature = FoSte = 3(r* 1 1)2 + 2(r* 1)3 + (r* 1)3Ste 1 (r* 1)2Ste2 6 645r* The formula can be used for evaluation of the time of complete freezing of any liquid The formula can be used for evaluation of the time of complete freezing of any liquid Kern and Wells [91] A NA NA Constant wall temperature 3(2 )2 Fof(Ste 0)= 1(1 +1) The formula can be used for evaluation of the time of complete freezing of any liquid The formula can be used for evaluation of the time of complete freezing of any liquid Hill and Kucera [92] Semi- NA NA Constant wall analy- temperature tical A NA NA Constant wall Ste 3Bi 6 t* =Fo =(2 +1)/6Steand t* =Fo =(1 +1)(2 +1)/6 Milanez and Ismail temperature The formula can be used for evaluation of the time of complete freezing of any liquid Not applicable [93] 6 3Bi Graphical presentation of variation of the solid-liquid interface position with dimensionless Caldwell and Chan [94] N NA NA Constant wall temperature time Graphical presentation of variation of solidifaied mass fraction with time for different sphere radius, temperature of external HTF and different Bio numbers Ismail and Henriquez [95, 96] N NA NA Constant wall temperature The result can be used only for cases considered in the study Lin and Jiang [97] Bilir and İlken [98] Quasi- steady analysis N NA NA Constant wall temperature f f 12Ste The formula can be used for evaluation of the time of complete freezing of any liquid The formula can be used for evaluation of the time of complete freesing of water The result can be used only for cases considered in the study Chan and Tan [99] Teggar et al. [100] E Graphical presentation of variation of solidifaied fraction with time for three different bath temperature Assis et al. [101] Ismail and Moraes 2.25(FoSte)1/2]2 The formula can be used for evaluation of the time of complete freezing of any liquid The result can be used only for cases considered in the study [103] Rajeev and Das [104] ElGhnam et al. [105] N&E Water and its glycol mixtures Glass plastic MF = [1 Graphical presentation of results Chandrasekaran et al. E E Water, water nano- compositions Copper, glass, brass, stainless steel, plastic LDPE Graphical presentation of results Tabular and graphical presentation of results The result can be used only for cases considered in the study [106-109] Satishkumar et al. Water/GNP LDPE Tabular data can be used for validation of numerical simulation results [110] Analyti- NA NA CWT cal S t e f = FoSte = 6 + 6 S t e 32 1 + ... 123456 8 N N&E NA Parrafin wax RT27 NA Thin plastic Graphical presentation of variation of the solidification front with dimensionless time Not applicable N E NA Water NA Graphical presentation of the molten fraction variation with dimensionless time Graphical presentation of results The result can be used only for cases considered in the study The result can be used only for cases considered in the study NA N-hexadecade NA Fluminum Constant wall temperature Water bath with constant temperature Constant wall temperature Water bath with constant temperature Water bath with constant temperature Constant wall temperature HTF flow with constant temperature Water-ethylene glycol bath with constant temperature Water-ethylene glycol BCT Fo =t = tf = Fof = 0.5012181 × Ste 0.9070384 × Bi 0.1864788 × 0.9843633 fmin fmin Bi f=FofSte=1+ 1 fmax fmax Ste Bi 1 + exp(p 2 ) m (continued on next page)PDF Image | Journal of Energy Storage 27
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