Chapter 13, Problem 13.47P

Consider the cavities formed by a cone, cylinder, and sphere having the same opening size (d) and major dimension (L), as shown in the diagram.

(a) Find the view factor between the inner surface of each cavity and the opening of the cavity.
(b) Find the effective emissivity of each cavity, ${\epsilon }_e$ , as defined in Problem 13.43, assuming the inner walls we diffuse and gray with an emissivity of ${\epsilon }_w$ .
(c) For each cavity and wall emissivities of ${\epsilon }_w=0.5,0.7$ , and 0.9, plot ${\epsilon }_e$ as a function of the major dimension-to-opening size ratio. L/d, over a range from 1 to 10.