Chapter 13, Problem 13.93P

A small oven consists of a cubical box of dimension $L=0.1\text{m}$ , as shown. The floor of the box consists of a heater that supplies $P=400\text{W}$ . The remaining walls lose heat to the surroundings outside the oven. which maintains their temperatures at $T_3=400\text{K}$ . A spherical object of diameter $D=30\text{mm}$ is placed at the center of the oven. Sometime after the sphere is placed in the oven, its temperature is $T_1=420\text{K}$ . All surfaces have emissivities of 0.4.

(a) Find the following view factors: F₁₂, F₁₃, F₂₁, F₃₁, F₂₃, F₃₂, F₃₃.
(b) Determine the temperature of the floor and the net rate of heat transfer leaving the sphere due to radiation. Is the sphere under steady-state conditions?