I have to determine the cooling time of a pipe from its initial temperature $\vartheta_{\text{wall,}1}=500 \text{ °C}$ to the temperature $\vartheta_{\text{wall,}2}=150 \text{ °C}$. The cooling happens due to an air flow through the pipe with the temperature $\vartheta_{\text{inlet}} = 30{\text{ °C}}$ and due to contact to the air in the environment $\vartheta_{0} = 20{\text{ °C}}$ at the outer surface of the pipe. Is there a quick way to estimate it? I thought about using Newton's Law of cooling but the problem is the heat transfer coefficient.

Data for inlet:

  • Inlet temperature: $\vartheta_{\text{inlet}} = 30{\text{ °C}}$
  • $p_{\text{inlet}} = 4 \text{ bar}$
  • $u_{\text{in}} = 5 \text{ m/s}$

Geometric/matrerial data of pipe:

  • Initial wall temperature (assumed to be constant) $\vartheta_{\text{Wall},1}=500 \text{ °C}$
  • Outer diameter $D_\text{o}=0.0210 \text{ m}$
  • Wall thikness $t = 0.0005 \text{ m}$
  • Length $L = 0.2000 \text{ m}$
  • Material not sure about it lets assume is some steel material

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