Project ForgeThree sets of parallel plates LM, NR and PQ are given in three figures. The view factor F_IJ is defined as the fraction of radiation leaving plate I that is intercepted by plate J. In Figure 1, plate L (1m wide) is centered 1m directly above plate M (3m wide, in three 1m segments). In Figure 2, plate N (1m wide) is directly above plate R (1m wide, same width and alignment), 1m apart. In Figure 3, plate P (1m wide) is flush with the left edge of plate Q (2m wide, in two 1m segments), 1m apart. Assume that the values of F_LM and F_NR are 0.8 and 0.4, respectively. The value of F_PQ (round off to one decimal place) is ___.
Explanation
Using the crossed-strings method, F(1→2)=[(sum of crossed strings)−(sum of uncrossed strings)]/(2×width of surface 1). For Figure 3 with P=(0,1)-(1,1), Q=(0,0)-(2,0): crossed strings sum to √5+√2, uncrossed strings sum to 1+√2, giving F_PQ=(√5−1)/2≈0.618→0.6. (As a consistency check, the same method reproduces the given F_LM=√5−√2≈0.82→0.8 and F_NR=√2−1≈0.41→0.4 exactly.)
Source: GATE ME 2019 Session 2 (Set 3) (2019)
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