A cast-iron pipe (λ = 51.0W/K m) with internal diameter d i = 40 mm and wall thickness δ = 7.5 mm is filled with water which is at a temperature of ϑ E = 0.0 ◦C. The external air is at ϑ 0 = −8.0 ◦C;...

A cast-iron pipe (λ = 51.0W/K m) with internal diameter d_i
= 40 mm and wall thickness δ = 7.5 mm is filled with water which is at a temperature of ϑ_E
= 0.0 ◦C. The external air is at ϑ₀
= −8.0 ◦C; the heat transfer coefficient between the pipe and air is α = 25W/m²
K. How long does it take for an ice layer of thickness s = 15 mm to form in the pipe, such that the increase in the volume of the ice compared to the water can lead to a burst pipe? How long will it take before the contents of the pipe are completely frozen? Properties of ice at 0 ◦C: = 917 kg/m³, λ = 2.25W/K m, h_E
= 333 kJ/kg.