Question
A flat plate made of cast iron is exposed to a solar flux of 600 W/m2 at an ambient temperature of 25°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 ×10–8 W/m2–K4. Neglect all other modes of heat transfer except radiation. Under the aforementioned conditions, the radiation equilibrium temperature of the plate is __________ °C (round off to the nearest integer)
Answer :
Correct answer is : 218
Solar flux, Gs = 600 W/m2
σ = 5.669 × 10-8 W/m2-K4
ambient Temperature Ta = 25∘C = 298 K
Surface temperature Ts
absorptivity, α = 0.21
Since the entire solar flux is absorbed by the plate and for steady-state of the slab, by Kirchoff's Law :
Heat absorbed by the plate = net heat transfer between plate and ambient
α = ϵ = 0.21
Gs = qrad = ϵσ (Ts4 - Ta4 )
600 = 0.21 × 5.669 × 10-8 (Ts4 - (298)4)
Ts = 491 K = 491 - 273 K
Ts = 218° C
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