Question

In an enclosure there are 8 surfaces. How many individual radiation view factors are involved?

• A. 8
• B. 16
• C. 32
• D. 64

Hint:

In an enclosure with \( N \) surfaces, the total number of view factors is \( N^2 \), accounting for all pairs \( (i, j) \), including self-viewing factors.

Answer 1

The Correct Option is D

Step 1: Understand radiation view factors.
In an enclosure with \( N \) surfaces, the view factor \( F_{ij} \) represents the fraction of radiation leaving surface \( i \) that is directly intercepted by surface \( j \). The view factor \( F_{ij} \) exists for every pair of surfaces, including self-viewing factors (\( F_{ii} \), which may be zero if the surface is flat or convex). Step 2: Calculate the total number of view factors.
For \( N \) surfaces, the total number of view factors is the number of possible pairs \( (i, j) \), including self-viewing factors.
The number of view factors is given by \( N \times N \), because each surface \( i \) can radiate to each surface \( j \), including itself: \[ \text{Total view factors} = N^2. \] Here, \( N = 8 \): \[ N^2 = 8 \times 8 = 64. \] Step 3: Consider the nature of individual view factors.
"Individual radiation view factors" typically refers to all possible \( F_{ij} \), including \( F_{ii} \).
In practice, some view factors may be zero (e.g., \( F_{ii} = 0 \) for flat or convex surfaces), and reciprocity (\( A_i F_{ij} = A_j F_{ji} \)) reduces the number of independent view factors. However, the question asks for the total number of view factors involved, which is \( N^2 \). Step 4: Evaluate the options.
(1) 8: This might represent the number of surfaces, not view factors. Incorrect.
(2) 16: This might be a miscalculation (e.g., \( 8 \times 2 \)). Incorrect.
(3) 32: This might be a miscalculation (e.g., \( 8 \times 4 \)). Incorrect.
(4) 64: Matches \( 8 \times 8 \), the total number of view factors. Correct.
Step 5: Select the correct answer.
For 8 surfaces, the total number of individual radiation view factors is \( 8 \times 8 = 64 \), matching option (4).