Question

1(30%). A thin plate black body, insulated at the bottom is placed faced up in a room with wall temperatures of 30 C. Air at 0 C is forced over the plate with a convective heat transfer coefficient of 12 W/m².C. Calculate the plate temperature under steady state condition

Answer 1

Explanation:

The given data is as follows.

         Heat transfer coefficient (h) = 12$W/m^{2}.C$

         Plate temperature ($T_{1}$) = $30 ^{o}C$ = 303 K

         Steady state temperature ($T_{2}$) = ?

Hence, formula applied for steady state is as follows.

       $(h \times A \times \Delta T)_{air}$ = $\sigma \times A \times (T^{4}_{1} - T^{4}_{2})_{plate}$

Putting the given values into the above formula as follows.

       $(h \times A \times \Delta T)_{air}$ = $\sigma \times A \times (T^{4}_{1} - T^{4}_{2})_{plate}$

        $12 \times (T_{2} - 273)$ = $5.67 \times 10^{-8} \times [(30 + 273)^{4} - T^{4}_{2}]$

                  $T_{2}$ = 282.66 K

                              = (282.66 -273)$^{o}C$      

                              = 9.66 $^{o}C$      

Thus, we can conclude that the steady state temperature will be 9.66 $^{o}C$.