How to estimate cooling time of pipe due to inner flow (instationary heat transfer)

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