. (20 pts) A horizontal cylindrical pipe (k = 10 W/m·K) has an outer diameter of 15 cm and a wall thickness of 5 cm. The pipe is
situated in a stationary air, where the air and surrounding temperature is 27°C. The outer surface temperature of the pipe is 127°C, and the pipe surface has an emissivity of 0.5. Determine the inner surface temperature of the pipe. Use the following air properties for the analysis: k = 0.03 W/m∙K, ν = 20.92 × 10−6 m2 /s, α = 29.90 × 10−6 m2 /s, Pr = 0.70
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Answer:
And replacing in the Carnot efficiency we got:
Explanation:
For this case we can use the fact that the maximum thermal efficiency for a heat engine between two temperatures are given by the Carnot efficiency:
We have on this case after convert the temperatures in kelvin this:
And replacing in the Carnot efficiency we got:
And the maximum power output on this case would be defined as:
Where represent the heat associated to the deposit with higher temperature.