A room is initially at the outdoor temperature of 25^degreeC. Now a large fan th

Question

A room is initially at the outdoor temperature of 25^degreeC. Now a large fan that consumes 200 W of electricity when running is turned on. The heat transfer rate between the room and the outdoor air is given as q =UA(T_i- T_o) where U =6 W/m^2 degreeC is the overall heat transfer coefficient, A =30 m^2 is the exposed surface area of the room, and t_i and T_0 are the indoor and outdoor air temperatures, respectively. Determine the indoor air temperature when steady operating conditions are established.

Explanation / Answer

Given:--- Initial temperature of room =Outdoor Temperature (To)=25oC

overall heat transfer coefficient(U)=6W/m2-oC Exposed surface -Area of room (A)=30 m2.

At steady state the energy consumed by the fan = Heat transfer brtween room and outdoor air

Energy consumed by fan = 200W

So 200= -UA(Ti-To) (Ti is the steady state indoor temperature of room);-ve is to indicate that the indoor room temperature is less than the out-door teperature.

200 = -6 * 30 * (Ti-25)

Ti-25= -1.111

Ti=25-1.111 = 23.889 oC

the steady state indoor  temperature of room=23.889 oC

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