Common Data for QuestionsRadiative heat transfer is intended between t...
Given Data:
- Temperature of plate 1 (T1) = 727°C = 1000 K
- Temperature of plate 2 (T2) = 227°C = 500 K
- Emissivity of plate 2 (ε2) = 0.7
- Stefan-Boltzmann constant (σ) = 5.67 * 10^-8 W/m^2K^4
Assumptions:
- The surfaces of the plates are sufficiently large to form a two-surface enclosure.
- Steady-state conditions exist.
Explanation:
Radiative heat transfer between two surfaces can be calculated using the Stefan-Boltzmann law, which states that the net heat transfer between two surfaces is proportional to the difference in their temperatures raised to the fourth power.
Calculating Irradiation:
Irradiation is defined as the amount of radiant energy incident on a unit area of a surface. In this case, we need to calculate the irradiation for plate 1.
The irradiation for plate 1 can be calculated using the following formula:
I1 = σ * ε1 * (T1^4 - T2^4)
Here, ε1 is the emissivity of plate 1. Since plate 1 is a black surface, its emissivity is assumed to be 1.
Substituting the given values into the formula, we have:
I1 = 5.67 * 10^-8 * 1 * (1000^4 - 500^4)
I1 = 5.67 * 10^-8 * (10^12 - 10^8)
I1 = 5.67 * 10^-8 * (999,999,999,999,900)
Simplifying the Calculation:
To simplify the calculation, we can approximate 999,999,999,999,900 as 10^15.
I1 ≈ 5.67 * 10^-8 * 10^15
I1 ≈ 5.67 * 10^7
Converting to kW/m2:
Since the unit of irradiation is W/m2, we need to convert the value to kW/m2. To do this, we divide the value by 1000.
I1 ≈ 5.67 * 10^7 / 1000
I1 ≈ 5.67 * 10^4 kW/m2
Final Answer:
Therefore, the irradiation for the upper plate (plate 1) is approximately 5.67 * 10^4 kW/m2.
Correct Option:
The correct answer is option 'D'.
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