Chapter 13, Problem 13.102P

Electrical conductors, in the form of parallel plates of length $L=40\text{mm}$ , have one edge mounted to a ceramic insulated base and are spaced a distance $w=10\text{mm}$ apart. The plates are exposed to large isothermal surroundings at $T_{\text{sur}}=300\text{K}$ . The conductor (1) and ceramic (2) surfaces are diffuse and gray with emissivities of ${\epsilon }_1=0.8$ and ${\epsilon }_2=0.6$ , respectively. For a prescribed operating current in the conductors, their temperature is $T_1=500\text{K}$ .

(a) Determine the electrical power dissipated in a conductor plate per unit length, ${q^{\prime }}_1$ , considering only radiation exchange. What is the temperature of the insulated base, T₂?
(b) Determine ${q^{\prime }}_1$ and T₂when the surfaces experience convection with an airstream at 300 K and a convection coefficient of $h=25{\text{W/m}}^2\cdot \text{K}$ .