Answer:
The expression for the exposed surface temperature is [tex] T_{0}=T_{\infty}+\dfrac{R_{fin}}{R_{ins}+R_{fin}}(T_{w}-T_{\infty})[/tex]
Explanation:
Given that,
Diameter = 25 mm
Conductivity = 60 W/mK
Temperature of wall = 200°C
Thickness = 200 mm
maximum temperature = 100°C
Temperature of ambient air = 30°C
Convection coefficient = 17.0 W/m²K
We need to calculate the heat transfer equation
Using diagram of thermal circuit
[tex]q_{f}=\dfrac{T_{0}-T_{\infty}}{R_{fin}}[/tex]
[tex]\dfrac{T_{0}-T_{\infty}}{R_{fin}}=\dfrac{T_{w}-T_{\infty}}{R_{ins}+R_{fin}}[/tex]
[tex]T_{0}-T_{\infty}=\dfrac{R_{fin}}{R_{ins}+R_{fin}}(T_{w}-T_{\infty})[/tex]
[tex]T_{0}=T_{\infty}+\dfrac{R_{fin}}{R_{ins}+R_{fin}}(T_{w}-T_{\infty})[/tex]
Hence, The expression for the exposed surface temperature is [tex] T_{0}=T_{\infty}+\dfrac{R_{fin}}{R_{ins}+R_{fin}}(T_{w}-T_{\infty})[/tex]
