# 2) When ice fishing, you need to use an auger to drill a hole in the ice.

2) When ice fishing, you need to use an auger to drill a hole in the ice. Many people do not enjoying augering, so you go on a mission to design a new system that melts a hole in the ice using an electric heater that is activated by your truck battery. The heater is attached to a 0.25 m diameter plate on one side and insulation on the other. You can assume that the heater is thin, and that there is no temperature gradient across it. Also assume that no heat is being lost through the edges of your system. An image of the design with all relevant dimensions and material properties is below:

The surface of the insulation experiences convection with the surrounding air at ????∞=5℃ and ℎ=50 ????/????2????. The new ice auger is placed on the ice, causing heat transfer to the plate-ice interface. Assume that the water under the ice is at ????????????????=0℃ so that no heat is conducted away from the plate-ice interface (all of the energy transferred to the plate-ice interface goes into melting the ice). You know the ice has density of ????????????????=920 ????????????3⁄ and the latent heat of fusion for ice is Δ????????????????=333.6 ????????????????⁄.

a. Determine the heat transfer rate to the plate-ice interface.

b. How long will it take to melt a hole in the ice?

c. What is the efficiency of the melting process?