Chapter 13, Problem 13.82P

A composite wall is comprised of two large plates separated by sheets of refractory insulation, as shown in the schematic. In the installation process, the sheets of thickness $L=50\text{mm}$ and thermal conductivity $k=0.05\text{W/m}\cdot \text{K}$ are separated at 1-m intervals by gaps of width $w=10\text{mm}$ . The hot and cold plates have temperatures and emissivities of $T_1=400°\text{C}$ , ${\epsilon }_1=0.85$ and $T_2=35°\text{C}$ , ${\epsilon }_2=0.5$ , respectively. Assume that the plates and insulation are diffuse-gray surfaces.

(a) Determine the heat loss by radiation through the gap per unit length of the composite wall (normal to the page).
(b) Recognizing that the gaps are located on a 1-m spacing, determine what fraction of the total heat loss through the composite wall is due to transfer by radiation through the insulation gap.