A cylindrical furnace has 0.1 m inner diameter and 0.2 m height. Walls A₁ (inner section of cylindrical surface area) and A₂ (inner section of 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 (A₃) is open to atmosphere maintained at 300 K, resulting in loss of heat 'q'.
Given: View factors F₁₃ = 0.1175 and F₂₃ = 0.06, where F_ij is the fraction of radiation leaving surface 'i' that is intercepted by surface 'j'.
Stefan-Boltzmann constant = 5.67 × 10⁻⁸ W/m²-K⁴.
The power needed to maintain the furnace at 1873 K, is (approximate to the nearest integer) __________________W.