## Case 2 Flow Under an Ice Cover

When an ice cover forms, the heat transfer from the underlying water to the ice proceeds at a constant rate that is not influenced by the air temperature or the presence or absence of a snow cover on top of the ice. This is because the ice surface, at the interface with the water, remains at 32°F (0°C) until all of the water is frozen. The rate of ice formation is influenced by the air temperature and the presence or absence of snow, but the cooling rate of the underlying water is not. The wetland water temperature under an ice cover can be estimated with Equation 6.17. This is identical in form to Equation 6.25, except for changes in two of the terms (Tm and U) to reflect the presence of the ice cover:

Tw = Tm + (T - Tm) exp[-Ui (x - X) )/Syvcp ] (6.17)

where

T0 = Water temperature at distance x0, assuming 37.4°F (3°C) where an ice cover commences.

Ui = Heat-transfer coefficient at ice/water interface (Btu/ft2-hr-°F; W/m2-°C).

Other terms are as defined previously.

The Ut value in Equation 6.17 depends on the depth of water beneath the ice and the flow velocity:

where

Ui = Heat-transfer coefficient at ice/water interface (Btu/ft2-hr-°F; W/m2-°C). O = Proportionality coefficient = 0.0022 Btu/ft26-hr02-°F (1622 J/m26-s02-°C).

v = Flow velocity (ft/hr; m/s), assuming no ice conditions. y = Depth of water (ft; m).

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