Consider a thermal storage system in which the phase change material (paraffin) is housed in a large container whose bottom, horizontal surface is maintained at T_s = 50°C by warm water delivered from a solar collector.

(a) Neglecting the change in sensible energy of the liquid phase, estimate the amount of paraffin that is melted over a five-hour period beginning with an initial liquid layer at the bottom of the container of thickness s₁ = 10 mm. The paraffin of Problems 8.47 and 9.57 is used as the phase change material and is initially at the phase change temperature, T_mp = 27.4^oC. The bottom surface area of the container is A = 2.5 m².

(b) Compare the amount of energy needed to melt the paraffin to the amount of energy required to increase the temperature of the same amount of liquid from the phase change temperature to the average liquid temperature, (T_s + T_mp)/2.

(c) Neglecting the change in sensible energy of the liquid phase, estimate the amount of paraffin that would melt over a five-hour time period if the hot plate is placed at the top of the container and S_i = 10mm.