Consider the phase change material (PCM) of Problems 8.47 and 9.57. The PCM is housed in a long, horizontal, and insulated cylindrical enclosure of diameter D_e = 200 mm, which in turn includes a concentric, heated inner cylinder of diameter D_i = 30 mm. Initially, the PCM is entirely solid and at its phase change temperature. The inner cylinder temperature is suddenly raised to T_h = 50°C. Assuming the PCM melts to form an expanding concentric liquid region about the heated tube such as the one shown in the schematic, determine how long it takes to melt half of the PCM.

Data From Problem 9.57

Consider Problem 8.47. A more realistic solution would  account for the resistance to heat transfer due to free  convection in the paraffin during melting. Assuming  the tube surface to have a uniform temperature of  55C and the paraffin to be an infinite, quiescent liquid,  determine the convection coefficient associated with the  outer surface. Using this result and recognizing that  the tube surface temperature is not known, determine the  water outlet temperature, the total heat transfer rate,  and the time required to completely liquefy the paraffin,  for the prescribed conditions. Thermophysical properties  associated with the liquid state of the paraffin are  k = 0.15 W/m · K,  β = 8 X 10^-4 K^-1, p = 770 kg/m³, v = 5 X 10^-6 m²/s, and α = 8.85 X 10^-8 m²/s.