To reduce heat transfer to a 6.0-m-long copper (k = 380 WmK) refrigerant line of 0.50...

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To reduce heat transfer to a 6.0-m-long copper (k = 380 WmK) refrigerant line of 0.50 cm inside diameter and 0.60 cm outside diameter, a plumber recommends that you insulate the line with a 1.0-cm-thick layer of Styrofoam insulation (k = 0.032 WmK). Refrigerant fluid at -40C flows inside the copper line with inside convective heat transfer coefficient of 500 WmK. The line is exposed to ambient air at 25C with outside convective heat transfer coefficient of 5.0 WmK-. a. Plot the rate of heat transfer to the line as a function of Styrofoam thickness. Would you accept the plumber's recommendation? b. Is the overall thermal resistance a monotonically increasing function of insulation thickness? If not, determine the insulation thickness that produces a local maximum or minimum in the overall thermal resistance. Can you provide a physical explanation for the observed behavior? c. Specify the thickness of Styrofoam insulation needed to reduce the heat transfer rate to the bare refrigerant line by 15 percent. What is the overall heat transfer coefficient for the insulated refrigerant line? d. If the thickness of the insulation layer cannot exceed 1.0 cm due to space limitations, what is the maximum allowable thermal conductivity of the insulating material that can be used to reduce energy loss? To reduce heat transfer to a 6.0-m-long copper (k = 380 WmK) refrigerant line of 0.50 cm inside diameter and 0.60 cm outside diameter, a plumber recommends that you insulate the line with a 1.0-cm-thick layer of Styrofoam insulation (k = 0.032 WmK). Refrigerant fluid at -40C flows inside the copper line with inside convective heat transfer coefficient of 500 WmK. The line is exposed to ambient air at 25C with outside convective heat transfer coefficient of 5.0 WmK-. a. Plot the rate of heat transfer to the line as a function of Styrofoam thickness. Would you accept the plumber's recommendation? b. Is the overall thermal resistance a monotonically increasing function of insulation thickness? If not, determine the insulation thickness that produces a local maximum or minimum in the overall thermal resistance. Can you provide a physical explanation for the observed behavior? c. Specify the thickness of Styrofoam insulation needed to reduce the heat transfer rate to the bare refrigerant line by 15 percent. What is the overall heat transfer coefficient for the insulated refrigerant line? d. If the thickness of the insulation layer cannot exceed 1.0 cm due to space limitations, what is the maximum allowable thermal conductivity of the insulating material that can be used to reduce energy loss?