A long cylindrical heater element of diameter D = 10 mm, temperature T₁ = 1500 K, and emissivity ?₁ = 1 is used in a furnace. The bottom area A₂ is a diffuse gray surface with ?₂ = 0.6 and is maintained at T₂ = 500 K. The side and top walls are fabricated from an insulating, refractory brick that is diffuse and gray with E = 0.9. The length of the furnace normal to the page is very large compared to the width wand height h. Neglecting convection and treating the furnace walls as isothermal, determine the power per unit length that must be provided to the heating element to maintain steady-state conditions. Calculate the temperature of the furnace wall.

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Heating element, A Furnace walls 60 h= 0.87 m Bottom, A om- -W= 1.0 m