Project ForgeHeat Transfer
Convection & Radiation
GATE 2013
Medium
Two large diffuse gray parallel plates, separated by a small distance, have surface temperatures of 400 K and 300 K. If the emissivities of the surfaces are 0.8 and the Stefan-Boltzmann constant is 5.67×10⁻⁸ W/m²K⁴, the net radiation heat exchange rate in kW/m² between the two plates is
- 0.66
- B0.79
- C0.99
- D3.96
Explanation
For two infinite parallel gray plates: q=σ(T1⁴−T2⁴)/(1/ε1+1/ε2−1). 1/0.8+1/0.8−1=1.5. T1⁴−T2⁴=400⁴−300⁴=2.56×10¹⁰−8.1×10⁹=1.75×10¹⁰. q=5.67×10⁻⁸×1.75×10¹⁰/1.5≈661.4 W/m²≈0.66 kW/m².
Source: GATE ME 2013 (Booklet Code A) (2013)
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