The figure shows a cylindrical furnace of inner diameter 0.1 m and height 0.2 m. The curved (lateral) side wall is surface \(A_1\), the bottom circular surface is \(A_2\), and the open top circular surface, facing the atmosphere, is \(A_3\).
A cylindrical furnace has 0.1 m inner diameter and 0.2 m height. Walls \(A_1\) (inner section of the cylindrical surface area) and \(A_2\) (inner section of the bottom surface area) are maintained at 1873 K. The sides and bottom are assumed to be black bodies, well insulated and heated electrically. The top area (\(A_3\)) is open to the atmosphere maintained at 300 K, resulting in loss of heat 'q'.
Given: View factors \(F_{13} = 0.1175\) and \(F_{23} = 0.06\), where \(F_{ij}\) is the fraction of radiation leaving surface 'i' that is intercepted by surface 'j'.
Stefan-Boltzmann constant \( = 5.67 \times 10^{-8} \) W/m\(^2\)-K\(^4\).
The power needed to maintain the furnace at 1873 K, is (approximate to the nearest integer) _______ W.