Icicles. Liquid water coats an active (growing)
icicle and extends up a short, narrow tube along
the central axis (Figure right). Because the water
ice interface must have a temperature of O°C, the
-Energy transfer
water in the tube cannot lose energy through the
sides of the icicle or down through the tip
because there is no temperature change in those
-Liquid coating
(OC)
- Liquid water
(0"C)
directions. It can lose energy and freeze only by
sending energy up (through distance L) to the top
of the icicle, where the temperature Tr can be
below O°C. Take L= 0.12 m and Tr =-5°C. Assume that the central tube and the
upward conduction path both have cross-sectional area A. In terms of A, what
rate is (a) energy conducted upward and (b) mass converted from liquid to ice at
the top of the central tube? (c) At what rate does the top of the tube move
downward because of water freezing there? The thermal conductivity of ice is
0.400W/m-K, and the density of liquid water is 1000 kg/m3