Two furnace designs, as illustrated and dimensioned in Problem 13.4, are used to heat a disk-shaped work piece (A₁). The power supplied to the conical and cylindrical furnaces (A₂) is 50 W. The work piece is located in a large room at a temperature of 300 K. and its back side is well insulated. Assuming all surfaces are black, determine the temperature of the work piece, T₁, and the temperature of the furnace inner surface, T₂ for each of the designs. In your analysis, use the expressions provided in Problem 13.4 for the view factors, F₂₁ and F₂₂.