In a pharmaceutical plant, a copper pipe (k_c= 400 W/m·K) with inner diameter of 20 mm and wall thickness of 2.5 mm is used for carrying liquid oxygen to a storage tank. The liquid oxygen flowing in the pipe has an average temperature of -200°C and a convection heat transfer coefficient of 120 W/m²·K. The condition surrounding the pipe has an ambient air temperature of 20°C and a combined heat transfer coefficient of 20 W/m²·K. If the dew point is 10°C, determine the thickness of the insulation (k_i= 0.05 W/m·K) around the copper pipe to avoid condensation on the outer surface. Assume thermal contact resistance is negligible.

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Liq. O2. -200°c h= 120 W/m?-K" -Pipe, k= 400 W/m-K Insulation k, = 0.05 W/m-K Surrounding air, 20°C hcombined = 20 W/m2K Dew point = 10°C DI = 20 mm D2 = 25 mm D3