Chapter 8, Problem 8.33P

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 $0°\text{C}$ , 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 $D=50mm$ , submerged in the bath.
(a) If air enters each tube at a mean temperature of $T_{m,i}=24°C$ and a flow rate of $\stackrel{\dot{}}{m}=0.01kg/s$ , what tube length L is needed to provide an exit temperature of $T_{m,o}=14°C$ ? With 10 tubes passing through a tank of total volume $V=10m^3$ , 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 $920kg/m^3$ and $3.34\times {10}^{5}J/kg$ , 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 $T_{m,o}$ as a function of $\stackrel{\dot{}}{m}\text{for}0.005\le \stackrel{\dot{}}{m}\le 0.05kg/s$ . If the dwelling cooled by this system requires approximately $0.05kg/s$ of air at $\text{16}°\text{C}$ , what design and operating conditions should be prescribed for the system?