Coated metallic disks are cured by placing them at thetop

Chapter 13, Problem 13.100

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Coated metallic disks are cured by placing them at thetop of a cylindrical furnace whose bottom surface iselectrically heated and whose sidewall may be approxi-mated as a reradiating surface. Curing is accomplishedby maintaining a disk at T2?400 K for an extendedperiod. The electrically heated surface is maintained atT1?800 K and is mounted on a ceramic base materialof thermal conductivity k?20 W/m?K. The bottom ofthe base material, as well as the ambient air and largesurroundings above the disk, are maintained at a tem-perature of 300 K. Emissivities of the heater and thedisk inner and outer surfaces are ?1?0.9, ?2,i?0.5,and ?2,o?0.9, respectively. Assuming steady-state operation and neglecting con-vection within the cylindrical cavity, determine theelectrical power that must be supplied to the heaterand the convection coefficient hthat must be main-tained at the outer surface of the disk in order to sat-isfy the prescribed conditions.