Chapter 13, Problem 13.100P

Coated metallic disks are cured by placing them at the top of a cylindrical furnace whose bottom surface is electrically heated and whose sidewall may be approximated as a reradiating surface. Curing is accomplished by maintaining a disk at $T_2=400\text{K}$ for an extended period. The electrically heated surface is maintained at $T_1=800\text{K}$ and is mounted on a ceramic base material of thermal conductivity $k=20\text{W/m}\cdot \text{K}$ . The bottom of the base material, as well as the ambient air and large surroundings above the disk, are maintained at a temperature of 300 K. Emissivities of the heater and the disk inner and outer surfaces are ${\epsilon }_1=0.9$ , ${\epsilon }_{2,i}=0.5$ , and ${\epsilon }_{2,o}=0.9$ , respectively.

Assuming steady-state operation and neglecting convection within the cylindrical cavity, determine the electrical power that must be supplied to the heater and the convection coefficient h that must be maintained at the outer surface of the disk in order to satisfy the prescribed conditions.