Consider a horizontal, thin-walled circular tube of diameter D = 0.025 m 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 it from the solid to liquid state at the phase change temperature of T∞ = 27.4°C. The latent heat of fusion and density of paraffin are hsf = 244 kJ/kg and p = 770 kg/m3 respectively, and thermo physical properties of the water may be taken as cp = 4.185 kJ/kg. K. k = 0.653 W/m ∙ K, μ = 467 x 10-6 kg/s ∙ m, and Pr = 2.99.

(a) Assuming the tube surface to have a uniform temperature corresponding to that of the phase change, determine the water outlet temperature and total heat transfer rate for a water flow rate of 0.1 kg/s and an inlet temperature of 60°C. If H = W = 0.25 m, how long would it take to completely liquefy the paraffin, from an initial state for which all the paraffin is solid and at 27.4°C?

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н Paraffin L= 3 m Water