Freezing a saturated liquid inside a sphere

Hill, James M.; Kucera, Adam

doi:10.1016/s0017-9310(83)80083-0

Cited by 57 publications

(21 citation statements)

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“…Ice growth in the model is based upon a quasi-steady state assumption that the timescale for heat conduction through the ice is short relative to the timescale of meteorological forcing (Patterson and Hamblin, 1988;Rogers et al, 1995). This assumption is valid under a Stefan number < 0.1 (Hill and Kucera, 1983). The ice module is applied when the simulated surface water temperature first drops below 0 • C; the initial ice thickness is set to a value of 5 cm to address effects of partial ice cover (Patterson and Hamblin, 1988;Vavrus et al, 1996).…”

Section: Hydrodynamic Modelmentioning

confidence: 99%

“…Increased water clarity can result in warmer deep waters (Stefan et al, 1996), while reduced light penetration can result in decreased mixing depth and cooler deep waters (Hocking and Straškraba, 1999;Tanentzap et al, 2008). Previous studies have also shown that increased water clarity was correlated with deeper mixed-layer depth Mazumder and Taylor, 1994;Schindler et al, 1996) and increased hypolimnetic heating rate (Yan, 1983).…”

Section: Introductionmentioning

confidence: 96%

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Trends and abrupt changes in 104 years of ice cover and water temperature in a dimictic lake in response to air temperature, wind speed, and water clarity drivers

Magee

Robertson

et al. 2016

Hydrol. Earth Syst. Sci.

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Abstract. The one-dimensional hydrodynamic ice model, DYRESM-WQ-I, was modified to simulate ice cover and thermal structure of dimictic Lake Mendota, Wisconsin, USA, over a continuous 104-year period (1911-2014). The model results were then used to examine the drivers of changes in ice cover and water temperature, focusing on the responses to shifts in air temperature, wind speed, and water clarity at multiyear timescales. Observations of the drivers include a change in the trend of warming air temperatures from 0.081 • C per decade before 1981 to 0.334 • C per decade thereafter, as well as a shift in mean wind speed from 4.44 m s −1 before 1994 to 3.74 m s −1 thereafter. Observations show that Lake Mendota has experienced significant changes in ice cover: later ice-on date(9.0 days later per century), earlier ice-off date (12.3 days per century), decreasing ice cover duration (21.3 days per century), while model simulations indicate a change in maximum ice thickness (12.7 cm decrease per century). Model simulations also show changes in the lake thermal regime of earlier stratification onset (12.3 days per century), later fall turnover (14.6 days per century), longer stratification duration (26.8 days per century), and decreasing summer hypolimnetic temperatures (−1.4 • C per century). Correlation analysis of lake variables and driving variables revealed ice cover variables, stratification onset, epilimnetic temperature, and hypolimnetic temperature were most closely correlated with air temperature, whereas freeze-over water temperature, hypolimnetic heating, and fall turnover date were more closely correlated with wind speed. Each lake variable (i.e., ice-on and ice-off dates, ice cover duration, maximum ice thickness, freeze-over water temperature, stratification onset, fall turnover date, stratification duration, epilimnion temperature, hypolimnion temperature, and hypolimnetic heating) was averaged for the three periods (1911-1980, 1981-1993, and 1994-2014) delineated by abrupt changes in air temperature and wind speed. Average summer hypolimnetic temperature and fall turnover date exhibit significant differences between the third period and the first two periods. Changes in ice cover (ice-on and iceoff dates, ice cover duration, and maximum ice thickness) exhibit an abrupt change after 1994, which was related in part to the warm El Niño winter of 1997-1998. Under-ice water temperature, freeze-over water temperature, hypolimnetic temperature, fall turnover date, and stratification duration demonstrate a significant difference in the third period , when air temperature was warmest and wind speeds decreased rather abruptly. The trends in ice cover and water temperature demonstrate responses to both long-term and abrupt changes in meteorological conditions that can be complemented with numerical modeling to better understand how these variables will respond in a future climate.Published by Copernicus Publications on behalf of the European Geosciences Union.

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Section: Hydrodynamic Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%

Trends and abrupt changes in 104 years of ice cover and water temperature in a dimictic lake in response to air temperature, wind speed, and water clarity drivers

Magee

Robertson

et al. 2016

Hydrol. Earth Syst. Sci.

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“…For S < 1, the quasisteady assumption can be shown to be valid I (Gilpin et al 1980;Hill and Kucera 1983). Several other specialized forms similar to the Maykut and Untersteiner (197 1) model have been documented.…”

mentioning

confidence: 94%

Thermal simulation of a lake with winter ice cover1

Patterson

Hamblin

1988

Limnology & Oceanography

118

103

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A one-dimensional thermodynamic model of a two-component ice and snow cover is added to an existing one-dimensional lake mixing model. Emphasis is placed on the thermodynamic coupling between the ice and mixing models-absent in previous models. The two-dimensional effects of partial ice cover are incorporated into this one-dimensional framework by using a minimum ice thickness. The model is applied to Lake Laberge, Yukon Territory, and to Babine Lake, British Columbia, for periods covering the formation and demise of full ice cover. The results of the model are compared to snow and ice measurements in the first case and to water column data during the spring period in the second. The comparisons are good, implying that the ice and snow model is performing satisfactorily and emphasizing the importance of the coupling between the ice and the underlying water. The successful simulation of the observed mixed layer under the ice, driven by convective stirring caused by short-wave heating below the temperature of maximum density, is an example of the ability of the model to provide physical insight into processes occurring in lakes.

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“…They also used this expression to determine upper and lower bounds of solidification/melting time of symmetric cylindrically shaped regions. Hill and Kucera [8] a spherical container. They included the effect of radiation at the container surface beside convection.…”

Section: Introductionmentioning

confidence: 99%

Total solidification time of a liquid phase change material enclosed in cylindrical/spherical containers

Bilir

İlken

2005

Applied Thermal Engineering

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This study investigates the inward solidification problem of a phase change material (PCM) encapsulated in a cylindrical/spherical container with a third kind of boundary condition. The governing dimensionless equations of the problem and boundary conditions are formulated and solved numerically by using enthalpy method with control volume approach. The problem is solved many times for different values of the affecting parameters and data sets are obtained for dimensionless total solidification time of the PCM. These data sets are then used to derive correlations which express the dimensionless total solidification time of the PCM in terms of Stefan Number, Biot Number and Superheat Parameter.

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Freezing a saturated liquid inside a sphere

Cited by 57 publications

References 10 publications

Trends and abrupt changes in 104 years of ice cover and water temperature in a dimictic lake in response to air temperature, wind speed, and water clarity drivers

Trends and abrupt changes in 104 years of ice cover and water temperature in a dimictic lake in response to air temperature, wind speed, and water clarity drivers

Thermal simulation of a lake with winter ice cover1

Total solidification time of a liquid phase change material enclosed in cylindrical/spherical containers

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