A right -circular cone and a right -circular cylinder of the same diameter and length (A2) are positioned coaxially at a distance Lo from the circular disk (A1) shown schematically. The inner base and lateral surfaces of the cylinder may be treated as a single surface, A2. The hypothetical area corresponding to the opening of the cone and cylinder is identified as A3.

(a) Show that, for both arrangements, F21 = (A1/A2) F13 and F22 = 1 - (A3/A2), where F13 is the view factor between two coaxial, parallel disks (Table).

(b) For L = Lo = 50 mm and D1 = D3 = 50 mm, calculate F21 and F22 for the conical and cylindrical configurations and compare their relative magnitudes. Explain any similarities and differences.

(c) Do the relative magnitudes of F21 and F22 change for the conical and cylindrical configurations as L increases and all other parameters remain fixed? In the limit of very large L, what do you expect will happen? Sketch the variations of F21 and F22 with L, and explain the key features.

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Relation Geometry * = XIL, F- Aligned Parallel Rectangles [a+x*)(+F]2 In +X (1 + F" tan (1 + y X tan"X - Ftan ' y +Y(1 +X" tun R = r/L. R, = rJL Coaxial Parallel Disks I+ R F, =IS- [S - (e,1r| Perpendicular Rectangles with a Common Edge H = ZIX, W YIX F, =w W tan" +tan - (H + w)" tan (H + W + wXI + H') 1+ Wi + H Hl + H + w) (1 + H'XH + Ww + w + H)w L1+wxw + Hy w1 D, D1 la) Right-circular cone (h) Right-circular cylinder