A grandmother is concerned about reducing her winter heating bills. Her strategy is to loosely fit rigid polystyrene sheets of insulation over her double-pane windows right after the first freezing weather arrives. Identify the relevant heat transfer processes on a cold winter night when the foamed insulation sheet is placed: (a) on the inner surface, and (13) 3 (b) on the outer surface of her window.

A common arrangement for heating a large surface area is to move warm air through rectangular ducts below the surface. The ducts are square and located midway between the top and bottom surfaces that are exposed to room air and insulated, respectively. For the condition when the floor and duct temperatures are 30C and 80C, respectively, and the thermal conductivity of concrete is 1.4 W/m*K, calculate the heat rate from each duct, per unit length of the duct. Use a grid spacing with delta x = 2*(delta y), where delta y = 0.125L and L=150mm.