Answer:
The surface temperature \( T_s \) can be calculated using the heat fluxes from conduction and convection:
Given:
[tex] \text{Thermal conductivity } k = 25 \ \text{W/m·K}[/tex]
[tex]text \: {Temperature \: gradient } \frac{dT}{dx} = -9000 \ \text{°C/m}[/tex]
[tex]text{Convection coefficient } h = 345 \ \text{W/m}^2\text{K}[/tex]
[tex]text \: {Surrounding \: temperature } \: T_\infty = 30 \ \text{°C}[/tex]
1. Heat flux by conduction:
[tex]q = -k \frac{dT}{dx} = -25 \times (-9000) = 225000 \ \text{W/m}^2[/tex]
2. Surface temperature by convection:
[tex]T_s = \frac{q}{h} + T_\infty = \frac{225000}{345} + 30 \approx 652.17 + 30 = 682.17 \ \text{°C}[/tex]
Thus, the surface temperature ( T_s ) is approximately
[tex]\( 682.17 \ \text{°C} \).[/tex]
