One cone is filled with ice and the other is filled with water. Lower the frozen cone into the water-filled cone to a height that optimizes the transfer of heat and minimizes the time it takes to thaw the ice.

At this point, the vertical distance from the vertex of the frozen cone to the water level is "h".

Assume that the portion of the frozen cone that is above the water level is insulated and loses no heat there; the only heat transfer is where the water touches the frozen cone.

(a) You are told to use a model which assumes that the heat transfer is proportional to the volume of the water remaining in the lower cone TIMES the surface area of the frozen cone which is touching water.

(b) If you have a different model employing a more accurate assumption with respect to the Physics involved, please state your assumption and solve, or if you prefer, submit a new problem with your model.

The Question: What is h (in terms of H)?