An atrium has a floor area of 30 m by 20 m and is 20 m high. The ceiling ventilation is designed for a fuel area of 30 m2 with an energy release rate of 0.5 MW/m2. The inlet openings are very large. An effective heat conduction coefficient can be assumed to be 20 W/m2°C.
(a) Calculate the area of ceiling vents required for ensuring a maximum thickness of the smoke layer of 5 m.
(b) A weak fire occurs in the atrium; a sofa burns for 3 minutes and releases energy at the constant rate of 500 kW. The ceiling vents are opened through signals from smoke detectors at the ceiling level, which activate at a temperature rise of 10°C. What will happen? Will the atrium be filled with smoke? How fast will this happen?
Please see the attachment for a step-by-step explanation.
Reference: http://fire.nist.gov/bfrlpubs/fire95/PDF/f95044.pdf and notes provided.
Qfl = 30*0.5 = 15 MW = 15*103 kW
hk = k/d
k = 20 W/m2/oC ...
The solution discusses energy release and ceiling ventilation in fire dynamics.