The wall of an old blast furnace for iron smelting consists of a 1.4 m thick layer of refractory bricks on the inside and a 12 cm thick steel layer on the outside. The temperature ti = 1500 C inside the furnace is considered constant. For sampling and control of the melting process, the furnace has a round opening with a diameter of d = 10 cm. Under the assumption that the opening is very small in relation to the inner volume of the furnace, the opening can approximately be considered a black body. a) Determine the heat loss Os, which is radiated to the surrounding area through the opening. (3) Note: If you are not able to determine Oy, continue with 0 = 4 kW. b) Determine the area Aw that would cause the same heat loss through heat transition at a constant ambient temperature of ta = 20 C. Aw can be considered a plane wall. Assume a heat transfer coefficient of (in = 230 W/(mK) on the inside and Clout = 15 W/(mK) on the outside. (4) c) Determine the temperature tw,out,b on the outside of the wall in case b). (2) d) Illustrate the qualitatively correct temperature profile of the heat transfer through the wall between the interior of the furnace and its surrounding environment. (3) lbrick = 0.6 W/(m-K), Isteel = 42 W/(m-K)