Three sets of parallel plates LM, NR and PQ are given in Figures 1, 2 and 3. The view factor FU is defined as the fraction of radiation leaving plate I that is intercepted by plate J. Assume that the values of FLM and FNR are 0.8 and 0.4, respectively. The value of FPQ (round off to one decimal place) is ___________.

 

The correct answer is 0.6.

To determine the view factor F_PQ for the configuration in Figure 3, we can use the principle of conservation of energy (view factor summation rule) and superposition (view factor addition rule) along with symmetry.

1. Analysis of Figure 1:
In Figure 1, the upper plate L has a length of 1 m. The lower plate M has a total length of 3 m and is positioned symmetrically below L at a distance of 1 m.
We can divide the lower plate M into three identical segments, each of length 1 m:
- M₁: the left segment of length 1 m
- M₂: the central segment of length 1 m, which is directly aligned below plate L
- M₃: the right segment of length 1 m

Using the view factor addition rule, the total view factor from plate L to plate M is the sum of the view factors from L to each of the three segments:

2. Analysis of Figure 2:
In Figure 2, the two parallel plates N and R are both of length 1 m and are aligned directly opposite to each other at a distance of 1 m. The view factor is given as:

Since the central segment M₂ of Figure 1 has the exact same size, alignment, and distance relative to plate L as the plates in Figure 2, we have:

3. Applying Symmetry to Figure 1:
Due to the symmetrical placement of plate L with respect to the outer segments M₁ and M₃, the view factors to these segments are equal:

Substituting these values back into the summation equation for Figure 1:

Simplifying the equation:

4. Analysis of Figure 3:
In Figure 3, the upper plate P of length 1 m radiates to a lower plate Q of length 2 m at a distance of 1 m.
We can partition plate Q into two segments, each of length 1 m:
- Q₁: the segment of length 1 m directly below plate P (this is identical to the configuration in Figure 2)
- Q₂: the segment of length 1 m offset to the right (this is identical to the configuration of segment M₃ relative to plate L in Figure 1)

Using the addition rule, the view factor F_PQ is:

Substituting the known view factors into the equation: