Answer
$\dot{Q}_{plates}=106,606.5\ Btu/s$
Work Step by Step
The energy balance for a single plate:
$Q=\Delta U=mc(T_2-T_1)$
With the mass given by:
$m=\rho (Ae)$
Given $\rho=532.5\ lbm/ft³,\ A=4ft²,\ e=1.6\ in$
We get the mass $m=284\ lbm$
Knowing $c=0.091\ Btu/lbm.°R, T_2=900°F,\ T_1=75°F$
We get: $Q_{plate}=21,321.3\ Btu$
For all plates (with a frequency $\dot{n}=300\ plates/min$
$\dot{Q}_{plates}=\dot{n}Q_{plate}$
$\dot{Q}_{plates}=6,396,390\ Btu/min=106,606.5\ Btu/s$
