Question

As shown in the figure, two large black plane surfaces are maintained at constant temperature $T_{1}$ and $T_{2}\left(T_{1} > \right.$ $T_{2}$ ). Two thin black plates are placed between the two surfaces and in parallel to them. After some time, steady conditions are obtained. The ratio of heat transfer rate between plate- $1$ and plate- $3$ to the ratio of original (when plate-$3$ and plate-$4$ was not present) heat tranfer rate between plate-$1$ and plate-$2$ in steady state is $\eta$. Find $\frac{1}{\eta}$.

Answer 1

$Q =\sigma\left(T_{1}^{4}-T_{3}^{4}\right) W / m ^{2}$
$=\sigma\left(T_{3}^{4}-T_{4}^{4}\right) W / m ^{2}$
$=\sigma\left(T_{4}^{4}-T_{2}^{4}\right) W / m ^{2}$
$3 Q =\sigma\left(T_{1}^{4}-T_{2}^{4}\right)=Q_{0} W / m ^{2}$
$\eta =\frac{Q}{Q_{0}}=\frac{1}{3}$