Ga copper pipe (kc = 400 w/m·k) with inner diameter of 20 mm and wall thickness of 0.025 m 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 (ki = 0.05 w/m·k) around the copper pipe to avoid condensation on the outer surface. assume thermal contact resistance is negligible.