A long cylindrical heater element of diameter D10 mm,

Chapter 13, Problem 13.73

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A long cylindrical heater element of diameter D?10 mm, temperature T1?1500 K, and emissivity ?1?1is used in a furnace. The bottom area A2is a diffuse,gray surface with ?2?0.6 and is maintained at T2?500 K. The side and top walls are fabricated from aninsulating, refractory brick that is diffuse and gray with??0.9. The length of the furnace normal to the pageis very large compared to the width wand height h.Neglecting convection and treating the furnace wallsas isothermal, determine the power per unit length that must be provided to the heating element to maintainsteady-state conditions. Calculate the temperature ofthe furnace wall.

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