A study of one-dimensional ice formation with particular reference to periodic growth and decay

Lock, G.S.H.; Gunderson, Jon; Quon, D.; Donnelly, J.K.

doi:10.1016/0017-9310(69)90021-0

Cited by 32 publications

(13 citation statements)

References 15 publications

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“…This problem, often referred to as the Stefan problem has a standard solution, which shows that the location of the phase change front, Y(s) is proportional to ffiffiffiffiffi as p where a is the thermal diffusivity [5]. Several variants of this problem have been addressed in past work, including a heat flux boundary condition [6][7][8][9][10][11], convective flow within the melted liquid [12,13], time-dependent temperature boundary condition [14][15][16], convective boundary condition [8], phase change over a temperature range [17], etc. Only the simplest of these phase change problems admits an exact solution-in most other cases, one must resort to approximate analytical methods that often result in series solutions.…”

Section: Introductionmentioning

confidence: 99%

“…A number of approximate solution methods are available for solving phase change problems [2,18]. For example, the perturbation method has been used to solve the problem with a timedependent boundary condition [14,15] as well as a problem with a constant heat flux boundary condition [8]. This method involves expressing the temperature distribution as a series solution involving powers of the Stefan number, and solving for each term individually.…”

Section: Introductionmentioning

confidence: 99%

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Solution of the Phase Change Stefan Problem With Time-Dependent Heat Flux Using Perturbation Method

Parhizi

Jain

2018

Journal of Heat Transfer

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Theoretical understanding of phase change heat transfer problems is of much interest for multiple engineering applications. Exact solutions for phase change heat transfer problems are often not available, and approximate analytical methods are needed to be used. This paper presents a solution for a one-dimensional (1D) phase change problem with time-dependent heat flux boundary condition using the perturbation method. Two different expressions for propagation of the phase change front are derived. For the special case of constant heat flux, the present solution is shown to offer key advantages over past papers. Specifically, the present solution results in greater accuracy and does not diverge at large times unlike past results. The theoretical result is used for understanding the nature of phase change propagation for linear and periodic heat flux boundary conditions. In addition to improving the theoretical understanding of phase change heat transfer problems, these results may contribute toward design of phase change based thermal management for a variety of engineering applications, such as cooling of Li-ion batteries.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Solution of the Phase Change Stefan Problem With Time-Dependent Heat Flux Using Perturbation Method

Parhizi

Jain

2018

Journal of Heat Transfer

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“…It is also found that the perturbation results obtained are identical with the exact solution for the limiting cases of boundary conditions. The method employed here is found to be simpler and more straight-forward in contrast to the perturbation methods employed by Lock and Huang [20][21][22]11] and also the method in [9]. The effect of Biot number on solidification and surface heat transfer is briefly discussed in the context of storing solar thermal energy using phase-change materials.…”

Section: Gefrieren Einer Warmen Striimenden Fliissigkeit In Ebener Fmentioning

confidence: 99%

“…Recently Weinbaum and Jiji [13] have presented perturbation solutions for the freezing of a finite domain above the melting point. A few references on the earlier application of different perturbation techniques are [16][17][18][19][20][21][22][23][24].…”

Section: Previous Workmentioning

confidence: 99%

Planar solidification of a warm flowing-liquid under different boundary conditions

Seeniraj

Bose

1982

Wärme- und Stoffübertragung

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Planar solidification of a warm flowing liquid with the convective heat transfer to the growing solid layer, has been analysed for the boundary conditions of constant temperature, constant heat flux and convective heat flux at the surface respectively. The mathematical formulation of the problem resuited in a coupled set of two differential equations in temperature and solid thickness as function of position, time and the problem parameters. Analytical expressions for the temperature distribution within the growing solid layer, the rate of solidification and the solidification time are obtained. The perturbation techniques employed here is simple and straight forward in contrast with the earlier techniques. Good agreement between the experimental results and the present solutions is obtained for the convective heat flux boundary condition. The results of this analysis are useful in the design and analysis of experiments dealing with freezing/melting in one dimension. The role of the parameter Stefan number which is small for phase change materials, is discussed in context with the storage of thermal energy. Gefrieren einer warmen, striimenden Fliissigkeit in ebener Front unter verschiedenen BedingungenZusammenfassung. Der Gefriervorgang einer warmen, str6men-den Fltissigkeit mit konvektivem W~irmeiibergang zur ebenen wachsenden Phasengrenze wurde mit den Randbedingungen konstante Temperatur, konstanter W~irmestrom und konvektiver W~irrnestrom an der Oberfl~iche untersucht. Man erh~ilt zwei gekoppelte Differentialgleichungen fiJr die Temperatur und die Dicke der festen Schicht als Funktion des Ortes, der Zeit und der Problemparameter. So gelangt man zu analytischen Ausdrticken ftir die Temperaturverteilung in der festen Schicht, der Geschwindigkeit und die Zeit der Erstarrung. Die hier angewandte St6-rungsrechnung ist einfach und, im Gegensatz zu ~ilteren Verfahren, explizit. Ffir konvektive fJbertragung als Randbedingung erh~ilt man gute Obereinstimmung zwischen Experiment und Theorie. Diese Ergebnisse sind wichtig fiir Entwurf und Auswertung yon experimentellen Resultaten mit Frieren und Schmelzen in einer Ebene. Der Einflug der Stefan-Zahl, die ffir in Frage kommende Stoffe klein ist, wird im Zusammenhang mit W~irme-speicherung untersucht.

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“…Since the phase change is controlled solely by the degree of supercooling at the cooling boundary and the convection heat flux from the liquid regime, it would be interesting to investigate the effects of a time-varying cooling temperature on the growth of the solid layer. In this regard, it should be mentioned that Lock et al [8] have studied a periodic solidification of water in a semi-infinite space.…”

mentioning

confidence: 99%

Solidification in a water‐saturated porous medium when convection is present (response of solid‐liquid interface due to time‐varying cooling temperature)

Okajima

Kiwata

Fusaoka

2006

Heat Trans. Asian Res.

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A fundamental study on solidifying phenomenon in a rectangular space filled with water-saturated porous medium has been carried out with a system, cooled from the upper boundary and heated from below, where vigorous convection develops in the un-solidified liquid layer. The dynamic response of the solid-liquid interface to the periodical cooling temperature with the bottom boundary kept at constant temperature T H = 20 °C, is investigated experimentally. In particular, the amplitude of the interface and the phase lag in respect to the oscillating cooling temperature have been monitored for various periods and average temperatures. A one-dimensional numerical model, based on an assumption of constant heat flux from the vigorously convecting liquid regime has been also developed. The numerical model predicts quite well the time-dependent behavior of the horizontally averaged ice-layer thickness observed in the experiments. Our general findings are that the amplitude increases proportionally to the temperature fluctuation period and that both the thicker solid layer and the shorter period cause greater phase lags.

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A study of one-dimensional ice formation with particular reference to periodic growth and decay

Cited by 32 publications

References 15 publications

Solution of the Phase Change Stefan Problem With Time-Dependent Heat Flux Using Perturbation Method

Solution of the Phase Change Stefan Problem With Time-Dependent Heat Flux Using Perturbation Method

Planar solidification of a warm flowing-liquid under different boundary conditions

Solidification in a water‐saturated porous medium when convection is present (response of solid‐liquid interface due to time‐varying cooling temperature)

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