Two thin wall metal pipes with an external diameter of 2.5 cm and joined by flanges that are 1.25 cm thick and 10 cm in diameter are carrying steam at 120oC. If the conductivity of the flange metal is k = 400 W/m-oC and the exposed surfaces of the flanges lose heat to the surroundings at T1 = 15oC according to a film heat transfer coefficient of h = 12 W/m2-oC, find the rate of heat loss from the pipe and the proportion of it that is transferred from the rim of the flange. Hint: First, derive the expression for the heat conducted from the pipe to the flange and also an expression for the heat lost through the rim using the general solution for the temperature profile in the flange. Then, write an Excel code with the above parameters as input to determine the heat loss rates and proportion.