Direction: Radiative heat transfer is intercepted between the inner surfaces of two very large isothermal parallel metal plates. While the upper plate (designated as plate 1) is a black surface and is the warmer one being maintained at 727°C, the lower plate (plate 2) is a diffuse and gray surface with an emissivity of 0.7 and is kept at 227°C. Assume that the surfaces are sufficiently large to form a two-surface enclosure and steady-state conditions to exist. Stefan-Boltzmann constant is given as 5.67 × 10-8W/m2K4.
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If plate 1 is also a diffuse and Gray surface with an emissivity value of 0.8, the net radiatibn heat exchange (in kW/m2) between plate 1 and plate 2 is
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- 17.0
- 19.5
- 23.0
- 31.7
Correct Option: D
= 0.59
∴ Q = f 12 σb (T14 – T24)
= 0.59 × 5.67 × (10000 – 625)
= 31362.18 W/m2
= 31.36 kW/m2
Alternately
1000 K = T A A (Black), εA = 0.8
500 K = TB B(Grey), εB = 0.7
Net heat exchange between A and B,
| Q = σ | |||||
| + | - 1 | ||||
| εA | εB | ||||
| = | × 5.67 × 10-8 | ||||
| + | - 1 | ||||
| 0.8 | 0.7 | ||||
| = | 1.25 + 1.4286 - 1 |
| = | × 5.67 × 10-8 | 1.6786 |
| = | W/m2 | 1.6786 |
≈ 31.7 kW/m2
