A long wooden rod at 38°C with a 2.5 cm OD is placed into an airstream at 600°C. The heat transfer coefficient between the rod and air is 28.4 W/(m2 K). If the ignition temperature of the wood is 427°C, ? = 800 kg/m3, k = 0.173 W/(m K), and c = 2500 J/(kg K), determine the time between initial exposure and ignition of the wood.

Question

GIVEN

• A long wooden rod is placed into an airstream

• Rod outside diameter (D) = 2.5 cm = 0.025 m

• Initial temperature of the rod (To) = 38°C

• Temperature of the airstream (T?) = 816°C

• The heat transfer coefficient (hc) = 28.4 W/(m2 K)

• The ignition temperature of the wood (TI) = 427°C

• Density of the rod (?) = 800 kg/m3

• Thermal conductivity (k) = 0.173 W/(m K)

• Specific heat (c) = 2500 J/(kg K)

FIND

• The time between initial exposure and ignition of the wood

SKETCH

Answer 1

The Biot number for the rod is



Therefore, the internal thermal resistance of the rod is significant and the approximate solutions will be used.



we have



For Bi=0.95 for Infinite cylinder, we have





solving for the time