In a pharmaceutical plant, a copper pipe (kc = 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 2200°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 (ki = 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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