Question

A metal pipe (kpipe=15W/mK,Di,pipe=5cm,Do,pipe=6cm,(kpipe = 15 W/m \cdot K, D_{i,pipe} = 5 cm, D_{o,pipe} = 6 cm, and L = 10 m) situated in an engine room is used for transporting hot saturated water vapor at a flow rate of 0.03 kg/s. The water vapor enters and exits the pipe at 325C325^\circ C and 290C,290^\circ C, respectively. Oil leakage can occur in the engine room, and when leaked oil comes in contact with hot spots above the oil’s autoignition temperature, it can ignite spontaneously. To prevent any fire hazard caused by oil leakage on the hot surface of the pipe, determine the needed insulation (kins=0.95W/mK)(k_{ins} = 0.95 W/m \cdot K) layer thickness over the pipe for keeping the outer surface temperature below 180C.180^\circ C.

Solution

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Given:\textbf{Given:}

  • kpipe=15WmKk_{pipe}=15 \hspace{1mm} \frac{\text{W}}{\text{mK}}
  • Di,pipe=5cm=0,05mD_{i,pipe}= 5\hspace{1mm} \text{cm}=0,05 \hspace{1mm} \text{m}
  • Do,pipe=6cm=0,06mD_{o,pipe}= 6 \hspace{1mm} \text{cm}=0,06 \hspace{1mm} \text{m}
  • L=10mL=10 \hspace{1mm} \text{m}
  • m˙=0,03kgs\dot{m}= 0,03 \hspace{1mm} \frac{\text{kg}}{\text{s}}
  • Te=290°CT_e=290 \hspace{1mm} \text{\textdegree}{\text{C}}
  • Ti=325°CT_i=325 \hspace{1mm} \text{\textdegree}{\text{C}}
  • kins=0,95WmKk_{ins}=0,95 \hspace{1mm} \frac{\text{W}}{\text{mK}}
  • Ts,o180°CT_{s,o} \leq 180 \hspace{1mm} \text{\textdegree}{\text{C}}

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