Answer
$\dot{Q}=4368.2\ kW$
Work Step by Step
The mass flowrate of steel is given by:
$\dot{m}=\rho A_1\mathcal{V}_1$
Since $\rho=7854\ kg/m³,\ A_1=(2\times0.005)m²,\ \mathcal{V}_1=10\ m/min$:
$\dot{m}=13.09\ kg/s$
Energy balance for the steel:
$\dot{m}h_1=\dot{m}h_2+\dot{Q}$
$\dot{Q}=\dot{m}c_p(T_1-T_2)$
With $c_p=0.434\ kJ/kg.K,\ T_1=820°C,\ T_2=51.1°C$
$\dot{Q}=4368.2\ kW$
