GATE Mechanical 2022 Set 1 | Question: 25

Question

A flat plate made of cast iron is exposed to a solar flux of $600\; W/m^{2}$ at an ambient temperature of $25^{\circ}C$. Assume that the entire solar flux is absorbed by the plate.

Cast iron has a low temperature absorptivity of $0.21$. Use Stefan-Boltzmann constant $= 5.669 \times 10^{-8}\; W/m^{2}- K^{4}$. Neglect all other modes of heat transfer except radiation.

Under the aforementioned conditions, the radiation equilibrium temperature of the plate is _____________$^{\circ}C$ (round off to the nearest integer).

 

Answer 1

According to Kirchoff's Law, when then body is in thermal equilibrium then the emissivity is equal to absorptivity ε=α=0.21
Also, Heat absorbed by the plate = net heat transfer between plate and ambient  

Gs = Qrad = ϵσ (T_s^4 - T_a^4 )

600 = 0.21 × 5.669 × 10-8 (Ts4 - (298)4)

Ts = 491 K = 491 - 273 K

Ts = 218∘ C