A room is initially at the outdoor temperature of 25°C. Now a large fan that con

Question

A room is initially at the outdoor temperature of 25°C. Now a large fan that consumes 200 W of electricity when running is turned on (Fig. 2–49). The heat transfer rate between the room and the outdoor air is given as

Welect. in Q      UA(Ti         To) where U     6 W/m2 · °C is the overall heat transfer coefficient,Fan

A      30 m2 is the exposed surface area of the room, and Ti and To are the indoor and outdoor air temperatures, respectively. Determine the indoor air temperature when steady operating conditions are established.

Explanation / Answer

A large fan is turned on and kept on in a room that looses heat to the outdoors. The indoor air temperature is to be determined when steady operation is reached. Assumptions 1 Heat transfer through the floor is negligible. 2 There are no other energy interactions involved. Analysis The electricity consumed by the fan is energy input for the room, and thus the room gains energy at a rate of 200 W. As a result, the room air temperature tends to rise. But as the room air temperature rises, the rate of heat loss from the room increases until the rate of heat loss equals the elec- tric power consumption. At that point, the temperature of the room air, and thus the energy content of the room, remains constant, and the conservation of energy for the room becomes ( E in E out ) dE system > dt Rate of net energy transfer Rate of change in internal, kinetic, by heat, work, and mass potential, etc., energies Welect,in Q out UA 1Ti To 2 200 W =(6 W/m2 .°C) (30 m2) (Ti -25°C2) it gives Therefore, the room air temperature will remain constant after it reaches 26.1°C.

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