The evaporator section of a heat pump is installed in a large tank of water, which is used as a heat source during the winter. As energy is extracted from the water, it begins to freeze, creating an ice/water bath at 0°C, which may be used for air conditioning during the summer. Consider summer cooling conditions for which air is passed through an array of copper tubes, each of inside diameter D = 50 mm, submerged in the bath.

(a) If air enters each tube at a mean temperature of Tm,i = 24°C and a flow rate of In = 0.01 kg/s, what tube length L is needed to provide an exit temperature of Tm,o = 14°C? With 10 tubes passing through a tank of total volume V = 10 m3, which initially contains 80% ice by volume, how long would it take to completely melt the ice? The density and latent heat of fusion of ice are 920 kg/m 3 and 3.34 x 105 J/kg, respectively.

(b) The air outlet temperature may be regulated by adjusting the tube mass flow rate. For the tube length determined in part (a), compute and plot Tm,o, as a function of In for 0.005 < m < 0.05 kg/so If the dwelling cooled by this system requires approximately 0.05 kg/s of air at 16°C, what design and operating conditions should be prescribed for the system?