A vertical, cylindrical tank is filled with water at 20^∘C. The tank is insulated at the top and bottom, with diameter of 0.5 m and height of 1.0 m. The overall heat transfer coefficient is U = 120 W/m² K. The density of water is ρ = 1000 kg/m³ ,the heat capacity C_p = 4180 J/kgK, the melting point is 0^∘C and the heat of fusion is λ = 334 kJ/kg. 

(a) In the evening, the tank is suddenly exposed to air at −15^∘ C. Calculate how many minutes it will take for the first crystal of ice to form in the tank. Model this process by assuming thermal equilibrium between the tank and the environment at an initial steady state, followed by a sudden drop in the outside temperature to−15^∘C.
(b) How long will it take to completely freeze the water in the tank? You many neglect any volume expansion associated with freezing and assume that the tank is well-mixed, that is, the temperature is uniform within the tank and there are no radial temperature gradients.