A radiation source is to be built, as shown in the diagram, for an experimental study of radiation. The base of the hemisphere is to be covered by a circular plate having a centered hole of radius R/2. The underside of the plate is to be held at 555 K by heaters embedded in its surface. The heater surface is back. The hemispherical surface is well-insulated on the outside. Assume gray diffuse processes and uniform distribution of radiation.
(a) Find the ratio of the radiant intensity at the opening to the intensity of emission at the surface of the heated plate.
(b) Find the radiant energy loss through the opening in watts for R = 0.3 m.
(c) Find the temperature of the hemispherical surface.
GIVEN
A radiation source as shown above
Radius of hole = R/2
Temperature of underside of plate (T2) = 555 K
Underside of plate is black
Hemispherical surface is well insulated on the outside
ASSUMPTIONS
Gray diffuse processes
Uniform distribution of radiation
Radiation entering A1 is negligible, i.e., A1 as a black body at 0 K
Heat loss through insulation is negligible