Consider a horizontal, thin-walled circular tube

Chapter 8, Problem 8.47

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Consider a horizontal, thin-walled circular tube ofdiameter D?0.025 m submerged in a container of n- octadecane (paraffin), which is used to store thermalenergy. As hot water flows through the tube, heat istransferred to the paraffin, converting it from the solidto liquid state at the phase change temperature ofT??27.4C. The latent heat of fusion and densityof paraffin are hsf?244 kJ/kg and ??770 kg/m3,respectively, and thermophysical properties of the watermay be taken as cp?4.185 kJ/kg?K, k?0.653 W/m?K,??467?10?6kg/s?m, and Pr?2.99.(a) Assuming the tube surface to have a uniform tem- perature corresponding to that of the phase change,determine the water outlet temperature and total heattransfer rate for a water flow rate of 0.1 kg/s and aninlet temperature of 60C. If H?W?0.25 m, howlong would it take to completely liquefy the paraffin,from an initial state for which all the paraffin is solidand at 27.4C?(b) The liquefaction process can be accelerated byincreasing the flow rate of the water. Computeand plot the heat rate and outlet temperature as afunction of flow rate for 0.1??0.5 kg/s. Howlong would it take to melt the paraffin form 0 ? .5kg/s?