Heat conduction with solidification and a convective boundary condition at the freezing front

Lapadula, C.A; Mueller, W.

doi:10.1016/0017-9310(66)90048-2

Cited by 39 publications

(5 citation statements)

References 3 publications

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“…1(a)) is given by δ(x) 4.2 D w x/u 0 for a plug flow [26] . Interestingly, contrary to former studies [24,27,28], this thermal boundary layer cannot develop infinitely since it is bounded by the rivulet thickness h w . It only exists for small x such that δ(x) < h w , leading to x 0.06 h 2 w u 0 /D w 2 cm, constant for all the experiments.…”

contrasting

confidence: 70%

Freezing a rivulet

Monier,

Huerre,

Josserand

et al. 2019

Preprint

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contrasting

confidence: 70%

Freezing a rivulet

Monier,

Huerre,

Josserand

et al. 2019

Preprint

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“…This nonlinear character of the problem has been the primary focus of analytical studies of phase change. It has been dealt with for phase change on a flat surface by Yen & Tien (1963), Libby & Chen (1965), Lapadula & Mueller (1966), Siegal & Savino (1966), Savino & Siegal (1969) and Beaubouef & Chapman (1967), and for phase change in a pipe by Zerkle & Sunderland (1968), ozisik & Mulligan (1969) and Stephan (1969). Also in the transient problems complications may result from the fact that the specific volumes of the solid and liquid phases are seldom the same.…”

Section: Japanmentioning

confidence: 99%

Wave formation and heat transfer at an ice-water interface in the presence of a turbulent flow

1980

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Under some conditions of temperature and flow an ice-water interface in the presence of a turbulent stream has been observed to be unstable. In this paper the source and the conditions for the instability were investigated for a well-defined turbulent boundary-layer flow. It was found that the instability resulted from the interaction that occurs between a wavy surface and a turbulent flow over it. Such an interaction results in a heat transfer variation which is 90 to 180 degrees out of phase with the surface wave shape – a result which is consistent with the calculations of Thorsness & Hanratty (1979a,b).The main factor controlling damping of the instability at an ice-water interface was found to be the rate at which heat is conducted away from the interface into the ice.In the past it has been found that when an ice layer is melting, that is when the heat conduction in the ice is small, the ice surface is highly unstable. In the present study it was found that for a sufficiently large temperature ratio (Tf−Tw)/(T∞−Tf), a steady-state ice layer is also unstable. Furthermore it is predicted, from the present observations, that a growing ice layer with a ratio of ice-side to water-side heat fluxes of up to 2.3 could be unstable.Under sufficiently unstable conditions waves on the ice surface grow to an amplitude at which flow separations occur near the wave crests. This results in a ‘rippled’ ice surface pattern very similar to the patterns observed on mobile bed surfaces (Kennedy 1969) or surfaces which are being dissolved into a flowing stream (Allen 1971). The development of a ‘rippled’ ice surface results in a very substantial increase in the mean heat-transfer rate which would have an important influence on predictions of ice formation in the presence of a turbulent stream.

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“…x, (t = 0) = 0 (5) Equation (5) corresponds to the initial condition of zerothickness at t = 0. Cases (a), (b) and (c) correspond to the boundary conditions of I, II and III kind respectively.…”

Section: Analysis and Resultsmentioning

confidence: 99%

“…However, a brief review pertinent to the present problem is presented. Libby and Chen [4] and Lapadula and Mueller [5] applied Goodman's integral and Blot's variational methods respectively to the growth of a solid layer deposited from a fluid flowing past a cold surface. Beaubouef and Chapman [6] and Siegel and Savino [7] have respectively presented numerical and exact analytical results to the above problem which corresponds to the boundary condition of !…”

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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Heat conduction with solidification and a convective boundary condition at the freezing front

Cited by 39 publications

References 3 publications

Freezing a rivulet

Freezing a rivulet

Wave formation and heat transfer at an ice-water interface in the presence of a turbulent flow

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

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