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Q6. A steel pipe carrying steam has an outside diameter of 89 mm. It is lagged with 76 mm of insulation having an average k = 0.043 W/m.K. Two thermocouples, one located at the interface between the pipe wall and the insulation and the other at the outer surface of the insulation, give temperatures of 115°C and 32°C, respectively. Calculate the heat loss in W per m of pipe. Q7. A metal steam pipe having an outside diameter of 30 mm has a surface temperature of 400 K and is to be insulated with an insulation having a thickness of 20 mm and a k of 0.08 W/m · K. The pipe is exposed to air at 300 K and a convection film coefficient of 30 W/m² · K. a) Calculate the critical radius and the heat loss per m of length for the bare pipe. b) Calculate the heat loss for the insulated pipe assuming that the surface temperature of the pipe remains constant. Q8. A reaction mixture having a Cpm = 2.85 kJ/kg.K is flowing at a rate of 7 260 kg/h and is to be cooled from 377.6 K to 344.3 K. Cooling water at 288.8 K is available and the flow rate is 4 536 kg/h. The overall heat transfer coefficient Uo is 653 W/m²K. a) For counterflow, calculate the outlet water temperature and the area Ao of the exchanger. b) Repeat calculations for cocurrent flow. Q9. Oil flowing at the rate of 7 258 kg/h with a Cpm = 2.01 kJ/kg · K is cooled from 394.3 K to 338.9 K in a countercurrent flow heat exchanger by water entering at 294.3 K and leaving at 305.4 K. Calculate the flow rate of the water and the overall heat transfer coefficient Ui if the Ai is 5.11 m². Q10. Water flowing at the rate of 13.85 kg/s is to be heated from 54.5 to 87.8°C in a heat exchanger by 54 430 kg/h of hot gas flowing countercurrent flow and entering at 427°C (Cpm = 1.005 kJ/kg · K). The overall heat transfer coefficient Uo = 69.1 W/m²K. Calculate the exit-gas temperature and the heat-transfer area. Q11. A plane wall is constructed of a material having a thermal conductivity that varies as the square of the temperature according to the relation k = k0(1 + ?T²). Derive an expression for the heat transfer in such a wall (k0 and ? are constants).

Q6. A steel pipe carrying steam has an outside diameter of 89 mm. It is lagged with 76 mm of insulation having an average k = 0.043 W/m.K. Two thermocouples, one located at the interface between the pipe wall and the insulation and the other at the outer surface of the insulation, give temperatures of 115°C and 32°C, respectively. Calculate the heat loss in W per m of pipe.
Q7. A metal steam pipe having an outside diameter of 30 mm has a surface temperature of 400 K and is to be insulated with an insulation having a thickness of 20 mm and a k of 0.08 W/m · K. The pipe is exposed to air at 300 K and a convection film coefficient of 30 W/m² · K.
a) Calculate the critical radius and the heat loss per m of length for the bare pipe.
b) Calculate the heat loss for the insulated pipe assuming that the surface temperature of the pipe remains constant.
Q8. A reaction mixture having a Cpm = 2.85 kJ/kg.K is flowing at a rate of 7 260 kg/h and is to be cooled from 377.6 K to 344.3 K. Cooling water at 288.8 K is available and the flow rate is 4 536 kg/h. The overall heat transfer coefficient Uo is 653 W/m²K.
a) For counterflow, calculate the outlet water temperature and the area Ao of the exchanger.
b) Repeat calculations for cocurrent flow.
Q9. Oil flowing at the rate of 7 258 kg/h with a Cpm = 2.01 kJ/kg · K is cooled from 394.3 K to 338.9 K in a countercurrent flow heat exchanger by water entering at 294.3 K and leaving at 305.4 K. Calculate the flow rate of the water and the overall heat transfer coefficient Ui if the Ai is 5.11 m².
Q10. Water flowing at the rate of 13.85 kg/s is to be heated from 54.5 to 87.8°C in a heat exchanger by 54 430 kg/h of hot gas flowing countercurrent flow and entering at 427°C (Cpm = 1.005 kJ/kg · K). The overall heat transfer coefficient Uo = 69.1 W/m²K. Calculate the exit-gas temperature and the heat-transfer area.
Q11. A plane wall is constructed of a material having a thermal conductivity that varies as the square of the temperature according to the relation k = k0(1 + ?T²). Derive an expression for the heat transfer in such a wall (k0 and ? are constants).

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