Chapter 13, Problem 13.32P

A radiometer views a small target (1) that is being heated by a ring-shaped disk heater (2). The target has an area of $A_1=0.0004{\text{m}}^{\text{2}}$ , a temperature of $T_1=500\text{K}$ , and a diffuse, gray emissivity of ${\epsilon }_1=0.8$ . The heater operates at $T_2=1000\text{K}$ and has a black surface. The radiometer views the entire sample area with a solid angle of $\text{ω}=0.0008\text{sr}$ .

(a) Write an expression for the radiant power leaving the target which is collected by the radiometer, in terms of the target radiosityJ₁and relevant geometric parameters. Leave in symbolic form.
(b) Write an expression for the target radiosityJ₁in terms of its irradiation, emissive power, and appropriate radiative properties. Leave in symbolic form.
(c) Write an expression for the irradiation on the target, G₁, due to emission from the heater in terms of the heater emissive power, the heater area, and an appropriate view factor. Use this expression to numerically evaluate G₁.
(d) Use the foregoing expressions and results to determine the radiant power collected by the radiometer.