A steel tube (k = 15 W/m.K) 3 m long carries a refrigerated liquid at 5°C. The inner diameter of the tube is 4 cm and the thickness is 1.5 cm. The convection heat transfer coefficient inside the tube is 80 W/m.K. The fluid receives heat from the external environment, which is at 28°C with a convection heat transfer coefficient of 20 W/m .K. To reduce the gain, it is studied to add a layer of insulating foam to the tube with a thickness of 5 cm and thermal conductivity k = 0.08 W/m.K. The placement of insulation pays off financially if the heat transfer rate is reduced by at least 30% and if the external surface temperature is above 15°C. Ignoring the effects of radiation, verify that these conditions are met.

A steel tube (k = 15 W/m.K) 3 m long carries a refrigerated liquid at 5°C. The inner diameter of the tube is 4 cm and the thickness is 1.5 cm. The convection heat transfer coefficient inside the tube is 80 W/m.K. The fluid receives heat from the external environment, which is at 28°C with a convection heat transfer coefficient of 20 W/m .K. To reduce the gain, it is studied to add a layer of insulating foam to the tube with a thickness of 5 cm and thermal conductivity k = 0.08 W/m.K. The placement of insulation pays off financially if the heat transfer rate is reduced by at least 30% and if the external surface temperature is above 15°C. Ignoring the effects of radiation, verify that these conditions are met.

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter2: Steady Heat Conduction

Section: Chapter Questions

Problem 2.49P

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2.30 An electrical heater capable of generating 10,000 W is to be designed. The heating element is to be a stainless steel wire having an electrical resistivity of ohm-centimeter. The operating temperature of the stainless steel is to be no more than 1260°C. The heat transfer coefficient at the outer surface is expected to be no less than in a medium whose maximum temperature is 93°C. A transformer capable of delivering current at 9 and 12 V is available. Determine a suitable size for the wire, the current required, and discuss what effect a reduction in the heat transfer coefficient would have. (Hint: Demonstrate first that the temperature drop between the center and the surface of the wire is independent of the wire diameter, and determine its value.)
2.38 The addition of aluminum fins has been suggested to increase the rate of heat dissipation from one side of an electronic device 1 m wide and 1 m tall. The fins are to be rectangular in cross section, 2.5 cm long and 0.25 cm thick, as shown in the figure. There are to be 100 fins per meter. The convection heat transfer coefficient, both for the wall and the fins, is estimated to be K. With this information determine the percent increase in the rate of heat transfer of the finned wall compared to the bare wall.
1.10 A heat flux meter at the outer (cold) wall of a concrete building indicates that the heat loss through a wall of 10-cm thickness is . If a thermocouple at the inner surface of the wall indicates a temperature of 22°C while another at the outer surface shows 6°C, calculate the thermal conductivity of the concrete and compare your result with the value in Appendix 2, Table 11.
A steel tube (k = 15 W/m.K) 3 m long carries a refrigerated liquid at 5°C. The inner diameter of the tube is 4 cm and the thickness is 1.5 cm. The convection heat transfer coefficient inside the tube is 80 W/m².K. The fluid receives heat from the external environment, which is at 28°C with a convection heat transfer coefficient of 20 W/m².K. To reduce the gain, it is studied to add a layer of insulating foam to the tube with a thickness of 5 cm and thermal conductivity k = 0.08 W/m².K. The placement of insulation pays off financially if the heat transfer rate is reduced by at least 30% and if the outside surface temperature is above 15°C. Ignoring the effects of radiation, verify that these conditions are met.
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A steel duct whose internal diameter is 5.0 cm, and external diameter is 7.6 cm and thermal conductivity is: k = 15.0 (W/(m ºC)) is covered with an insulating material whose thickness is 2.0 cm and of thermal conductivity k = 0.2 (W/(m ºC)). A hot gas flows through the interior of the duct at a temperature of 330.0 ºC that generates a heat transfer coefficient by forced convection h=400.0 (W/(m^2 · ºC)). The outer surface of the insulating layer is exposed to air whose temperature is 30.0 ºC with forced convection heat transfer surface h = 60.0 (W/(m^2 · °C)). As a process engineer and in charge of company operations, you have been asked to: i. Determine the heat loss experienced by the pipe along 10.0 m.ii. The temperature drops that are generated in the different thermal resistances of the system. That is, on the air side, the duct wall and on the hot gas side.