Respuesta :
The net radiation heat transfer between the two plates per unit surface area of the plates with shield and without shied are respectively; 2282.76 W/m² and 9766.75 W/m²
How to find the net radiation heat transfer?
We are given;
Temperature 1; T₁
Temperature 2; T₂
Temperature 3; T₃
Emissivity 1; ε₁ = 0.3
Emissivity 2; ε₂ = 0.7
Emissivity 3; ε₃ = 0.2
The net rate of radiation heat transfer with a thin aluminum shield per unit area of the plates with shield is;
Q'₁₂ = σ(T₁⁴ - T₂⁴)]/[((1/ε₁) + (1/ε₂) - 1) + ((1/ε₃,₁) + (1/ε₃,₂) - 1)]
Q'₁₂ = 5.67 * 10⁻⁸(900⁴ - 300⁴)/[((1/0.3) + (1/0.7) - 1) + ((1/0.15) + (1/0.15) - 1)]
Q'₁₂,shield = 2282.76 W/m²
The net rate of radiation heat transfer with a thin aluminum shield per unit area of the plates with no shield is;
Q'₁₂,no shield = σ(T₁⁴ - T₂⁴)]/((1/ε₁) + (1/ε₂) - 1))
Q'₁₂,no shield = 5.67 * 10⁻⁸(900⁴ - 300⁴)/[(1/0.3) + (1/0.7) - 1)]
Q'₁₂,no shield = 9766.75 W/m²
Then the ratio of radiation heat transfer for the two cases becomes;
Q'₁₂,shield/Q'₁₂,no shield = 2282.76/9766.75 = 0.2337 or 4/17
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