Chapter 13, Problem 13.4P

A right-circular cone and a right-circular cylinder of the same diameter and length (A₂) are positioned coaxially at a distance L_ofrom 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.

1. Right-circular cone

Right-circular cylinder

(a) Show that, for both arrangements, $F_{21}=\left(A_1/A_2\right)F_{13}$ and $F_{22}=1-\left(A_3/A_2\right)$ , where F₁₃is the view factor between two coaxial, parallel disks (Table 13.2).
(b) For $L=L_o=50\text{mm}$ and $D_1=D_3=50\text{mm}$ , calculate F₂₁and F₂₂for the conical and cylindrical configurations and compare their relative magnitudes. Explain any similarities and differences.
(c) Do the relative magnitudes of F₂₁and F₂₂change 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 F₂₁and F₂₂with L, and explain the key features.