Problem $1$:

The heating surface of a boiler is in contact with flue gas $($at $1200C)$ on one side and boiling water $($at $200C)$ on the other side. The metal wall thickness is $10mm$ and its thermal conductivity is $45\frac{W}{mK}.$ The convective heat transfer coefficient from the flue gas to the wall is $50\frac{W}{m^2(K)}$ and from the wall to the boiling water is $4000\frac{W}{m^2(K)}.$ Calculate the temperature at both surfaces of the metal wall.