GATE 2016 ME (ME3) – Question 52
Two large parallel plates having a gap of 10 mm in between them are maintained at temperatures T1 = 1000 K and T2 = 400 K. Given emissivity values, 𝜀1 = 0.5, 𝜀2 = 0.25 and Stefan-Boltzmann constant σ = 5.67 × 10−8 W/m2-K4, the heat transfer between the plates (in kW/m2) is __________ _________
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Correct answer: 10.9 to 11.2
Explanation
For large facing diffuse-gray plates, q″=σ(T₁⁴−T₂⁴)/(1/ε₁+1/ε₂−1). The denominator is2+4−1=5. Substitution gives5.67×10⁻⁸(1000⁴−400⁴)/5=11049.696W/m², or **11.0497kW/m²**. The vacuum-gap width does not enter this ideal radiation result.