Problem 21-1 - Example 21-1 A dry oak stick initially at...

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Example 21-1 A dry oak stick, initially at 50 ° F, is tossed on a fire. Assume the combustion gases in the fire are at 600 ° F and they flow over the stick with a velocity of 3 ft/s. If the stick is ½ in. in diameter, how long will it be before the surface reaches ignition temperature (451 ° F)? Btu = 0.11 hr ft °F oak k ⋅⋅ oak 3 lbm 34 ft ρ = , Btu 0.569 lbm°F p oak c = Neglect radiation. Solution: First find the heat transfer coefficient Re D µ = V Use air properties at the film temperature. The average surface temperature is: o 50 451 250 F 2 surf T + == o 250 600 = 425 F 22 surf fluid film TT T + + ρ = density (air, T = 425, P = 14.7) = 0.0448 lbm / ft 3 µ = viscosity (air, T = 425) = 0.064 lbm / ft·h
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Re = 3 lbm 0.5 ft 0.0448 ft 3 ft 12 315 lbm 1 h 0.064 ft h 3600 s s ⎛⎞ ⎜⎟ ⎝⎠ = From Table 12-1, if 40 < Re < 4000 Nu = 0.683 Re 0.466 Pr 0.333 hD k = () 0.683 k h D = Re 0.466 Pr 0.333 Pr = Prandtl (air, T = 425) = 0.696 k = conductivity (air, T = 425) = 0.0225 Btu hr ft R ⋅⋅ ( ) 0.466 0.333 Btu 0.0225 hr ft R 0.683 315 0.696 0.5 ft 12 h = h = 4.78 2o Btu hr ft F o Btu 0.5 4.78 ft hr ft F 2 12 0.905 Btu 0.11 hr ft F o oak hr Bi k == = Because Bi is not less than 0.1, the lumped system approximation
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Problem 21-1 - Example 21-1 A dry oak stick initially at...

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