The steam is in the red region and the blue region represents the metal pipe. Si

Question

The steam is in the red region and the blue region represents the metal pipe. Since metal is an excellent conductor of heat, it is assumed here that the temperatures at the inside and outside surfaces of the pipe are at the same temperature T1 (which is also the temperature of the steam = 212 oF). The yellow region represents insulation that is used to cut down on heat losses to the environment at temperature TA = 70 oF. The temperature on the insulation surface is TS, the outer radius of the metal pipe is R0 = 4 inches (.3333 ft) and the outer radius of the insulation is R.



Heat conduction through the insulation is modeled by Fourier’s Law:

(1)

where Q is the heat flow in BTU/hr, k is the thermal conductivity of the insulation, r is the distance coordinate in the radial direction and A is the heat transfer area which, for a cylinder, is A = 2rL where L is the length of the pipe. The heat transfer from the insulation surface to the ambient temperature TA is given by Newton’s Law of Cooling:

(2)

where h is a convective heat transfer coefficient. For this system, k = 0.04 BTU/hr ft oF and h = 10 BTU/hr ft2 oF. At steady state, conservation of energy requires that the heat flow rates Q for equations (1) and (2) must be equal.

Explanation / Answer

k

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