Answer :
Explanation:
The given data is as follows.
Heat transfer coefficient (h) = 12[tex]W/m^{2}.C[/tex]
Plate temperature ([tex]T_{1}[/tex]) = [tex]30 ^{o}C[/tex] = 303 K
Steady state temperature ([tex]T_{2}[/tex]) = ?
Hence, formula applied for steady state is as follows.
[tex](h \times A \times \Delta T)_{air}[/tex] = [tex]\sigma \times A \times (T^{4}_{1} - T^{4}_{2})_{plate}[/tex]
Putting the given values into the above formula as follows.
[tex](h \times A \times \Delta T)_{air}[/tex] = [tex]\sigma \times A \times (T^{4}_{1} - T^{4}_{2})_{plate}[/tex]
[tex]12 \times (T_{2} - 273)[/tex] = [tex]5.67 \times 10^{-8} \times [(30 + 273)^{4} - T^{4}_{2}][/tex]
[tex]T_{2}[/tex] = 282.66 K
= (282.66 -273)[tex]^{o}C[/tex]
= 9.66 [tex]^{o}C[/tex]
Thus, we can conclude that the steady state temperature will be 9.66 [tex]^{o}C[/tex].