Derive expressions for the view factor F₁₂ associated with the following arrangements. Express your results in terms of A₁, A₂, and any appropriate hypothetical surface area, as well as the view factor for coaxial parallel disks (Table 13.2, Figure 13.5).

  (a) A circular disk and a coaxial, ring-shaped disk.

  (b) A circular disk and a coaxial, right-circular cone. Sketch the variation of F₁₂ with θ for 0 < θ < π/2, and explain the key features.