Steam at a temperature of ϑ i = 600 ◦C flows in a tube of inner diameter d 1 = 0.25 m and outer diameter d 2 = 0.27 m made of a steel alloy (λ 1 = 16W/K m). The heat transfer coefficient is α i =...

Steam at a temperature of ϑ_i
= 600 ◦C flows in a tube of inner diameter d₁
= 0.25 m and outer diameter d₂
= 0.27 m made of a steel alloy (λ₁
= 16W/K m). The heat transfer coefficient is α_i
= 425W/m²K. The tube is insulated with a rock wool layer of thickness δ₂
= 0.05 m, on whose outer surface a hull of mineral fibres of thickness δ₃
= 0.02 m is attached. The heat transfer coefficient between the hull and the air at temperature ϑ_o
= 25 ◦C is α_o
= 30W/m²K. The thermal conductivity of the rock wool varies according to the temperature:

The mean thermal conductivity of the mineral fibre hull is λ_m3
= 0.055W/K m. Calculate the heat lost per length L of the tube Q/L ˙ and check whether the temperature of the mineral fibre hull is below the maximum permissible value of ϑ_max
= 250 ◦C.