Hot water at 50 ℃ is routed from one building in which it is generated to an adjoining building in which it is used for space heating. Transfer between the buildings occurs in a steal pipe (k = 60W/m ∙ K) of 100-mm outside diameter and 8-mm wall thickness. During the winter, representative environmental conditions involve air at T[infinity] = −5℃ and V = 3m/s in cross flow over the pipe. Account for the convection resistance associated with water flow at a mean velocity of um = 0.5m/s in the pipe. What is the heat loss per unit length of pipe?

To save energy, the air supply to a 2000 ft office has been shut off overnight and the room temperature has dropped to 40°f. in the morning, the thermostat is reset to 70°f and warm air at 120 f begins to flov in at 200ft'/min. the air is well mixed within the room, and an equal mass flow of air at room temperature (changing with time) is withdrawn through a return duct. the air pressure is nearly 1 atm everywhere. ignoring heat transfer with the surroundings and kinetic and potential energy effects, estimate how long it takes for the room temperature to reach 70°f. plot the room temperature as a function of time.