Chapter 8, Problem 8.47P

Consider a horizontal, thin-walled circular tube of diameter $D=0.0\text{25m}$ submerged in a container of n-octadecane (paraffin), which is used to store thermal energy. As hot water flows through the tube, heat is transferred to the paraffin, converting ii from the solid to liquid state at the phase change temperature of $T_{\infty }=27.4°\text{C}$ . The latent heal of fusion and density of paraffin are $h_{sf}=244\text{kJ/kg}$ and p = 770 kg/m. respectively, and thermophysical properties of the water may be taken as $c_p=4.185\text{kJ/kg}\cdot \text{K},k=0.653\text{W/m}\cdot \text{K},\mu =467\times {10}^{-6}\text{kg/s}\cdot \text{m}$ , and ${\mathrm{P}}_r=2.99$ .

1. Assuming the tube surface to have a uniform temperature corresponding to that of the phase change, determine the water outlet temperature ¡md total heat transfer rate fora water flow rate of $0.\text{1kg}/\text{s}$ and an inlet temperature of $\text{6}0°\text{C}$ . If $H=W=0.25$ m, how long would k take to completely liquefy the paraffin, from an initial state for which all the paraffin Is solid and at $\text{274}°\text{C}$?
2. The liquefaction process can be accelerated by increasing the flow rate of the water. Compute and plot the heat rate and outlet temperature as a function of flow rate for $0.1\le m\le 0.5\text{kg}/\text{s}$ . How long would it take to melt the paraffin for $m=0.\text{5kg}/\text{s}$