Answer
$\dot{Q}=408.91\ kW$
Work Step by Step
Treating the system as static with $\Delta t=1\ min$, we get a closed system with a $2\ m$ long cylinder.
The energy balance for the system is:
$Q=\Delta U=mc(T_2-T_1)$
With the mass given by:
$m=\rho.(L.\frac{\pi}{4}D^2 )$
Given $\rho=7833\ kg/m³, L=2\ m,\ D=0.08\ m$,
the mass is $m=78.75\ kg$.
Plugging in the values of: $c=0.465\ kJ/kg.K,\ T_2=700°C, T_1=30°C$:
we get $Q=24,534.56\ kJ$
Since $\dot{Q}=\frac{Q}{\Delta t}$
$\dot{Q}=408.91\ kW$
