A 2-in. schedule 40 steel pipe (ID=2.067in., OD = 2.375 in.) carries steam at 350F with a heat-transfer coefficient of 50 Btu/h*ft^2*F. The pipe is exposed to air at 70F with a heat-transfer coefficient of 2.0 Btu/h*ft^2*F. For safety reasons, as well as to conserve energy, it is desired to insulate the pipe so that the temperature of the surface exposed to air will be no greater than 120F. A commercial insulation vendor claims that using just 0.5 in. of his “high-efficiency” insulation will do the job. Is his claim correct? Notes:
1. The vendor’s literature states that a 6-in. thick layer of “high-efficiency” insulation has an R-value of 23.7.
2. The thermal resistance of the pipe wall may be neglected in this calculation. Also neglect contact resistance and thermal radiation effects
answer:
The schematic diagram of the pipe with insulation is given below with the inner radius R_{1}, Outer radius of pipe R_{2} and the radius of pipe with insulation R_{3}, here T is the temperature of the steam inside pipe.
From the question it is given that inner radius R_{1}, Outer radius of pipe R_{2} and the radius of pipe with insulation R_{3} vendor is claiming (we are considering 0.5 in thickness of the insulation to maintain wall temperature and decrease the heat transfer) are:
and other properties of pipe wall, insulative material and ambient air are g...
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