有木有人做过这道模拟题啊

sit310

Heat Transfer Fan
The diagram below shows a schematic diagram in 2-dimensions of a 3-dimensional situation. One has a house, which for simplicity is represented as a single room which is attached to a solar room. The solar room has no source of heat other than the warming that occurs due to sunlight. Even on very cold days the solar room will warm up after the sun rises (on clear days), cooling down when the sun sets or when it becomes cloudy. There is actually a door between this room and the rest of the house but here this fact will not be taken into account. The two spaces are connected by a heat transfer fan that is represented by F in the schematic. In the solar room there is a thermostat which activates the heat transfer fan when the temperature set by the homeowner is reached. When the temperature reaches r, the fan goes on and stays on until the temperature drops to r-m, where m might be 0. This fan then transfers air from the solar room to the house. The heat transfer fan is operated by electricity. The house is operated as a single zone by a gas or oil furnace. The house has a thermostat also, which when the heat falls below the temperature the home owner sets turns on the heat. The homeowner likes to set his thermostat during the heating season at t degrees. The system turns off after the temperature goes up k degrees, and when the temperature falls back down to exactly t, the cycle repeats.


(Diagram not to scale)
Making assumptions about the cost of gas (oil if oil is used) and electricity, the size of the rooms involved and the volume of air that the fan can transfer, and other parameters defined above or which you may choose to define, determine when taking advantage of the heat transfer fan will "save" the homeowner money. Make any additional assumptions about temperature patterns in which this system exists and about the walls of the rooms, etc., that you deem necessary.