Solve the below problem:
Q: In the design of buildings, energy conservation requirements dictate that the exterior surface area, A" be minimized. This requirement implies that, for a desired floor space, there may be optimum values associated with the number of floors and horizontal dimensions of the building. Consider a design for which the total floor space, Af' and the vertical distance between floors, Hf' are prescribed.
(a) If the building has a square cross section of width W on a side, obtain an expression for the value of W that would minimize heat los to the surroundings. Heat loss may be assumed to occur from the four vertical side walls and from a flat roof. Express your result in terms of Af and Hf'
(b) If Af = 32,768 m2 and Hf = 4 m. for what values of Wand Nf (the number of floors) is the heat loss minimized? If the average overall heat transfer coefficient is U = 1 W/m2 · K and the difference between the inside and ambient air temperatures is 25°C, what is the corresponding heat loss? What is the percent reduction in heat loss compared with a building for Nf = 2?