An unheated garage is placed on the north wall of a building to act as a thermal buffer zone. If the garage has roof area \(A_{p}\), window area \(A_{w i}\) door area \(A_{d}\), and wall area \(A_{w a}\) what is the effective \(U\) value for the north wall of the building if its area is \(A_{n}\) ? The garage floor is well insulated and has negligible heat loss. Express the effective \(U\) value in terms of the \(U\) values and areas of the several garage surfaces.