A row of regularly spaced cylindrical heating elements is used to maintain an insulated furnace wall at 500 K. The opposite wall is at a uniform temperature of 300 K. The insulated wall experiences convection with air at 450 K and a convection coefficient of 200 W/m² ? K. Assuming the walls and elements are black, estimate the required operating temperature for the elements.

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Wall, 300 K Heating element Insulated wall, 500 K 20 mm 10 mm