Liquid water coats an active (growing) icicle up a short, narrow tube along the central axis. Because the water-ice interface must have a temperature of 0 °C, the 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 directions. It can lose energy or freeze only by sending energy up (through a distance L) to the top of the icicle, where the temperature Tr can be below 0 °C.
Assume the central tube and the upward energy transfer path both have cross-sectional area A.
(a) What is the dominant type of energy transfer in this case? Explain.
(b) In terms of A, what rate is energy transferred upward?
(c) In terms of A, what mass is converted from liquid to ice at the top of the central tube?
(d) At what rate does the top of the tube move downward because of water freezing there?