Chapter 4 Transient Heat Conduction4-111The trunks of some dry oak trees are exposed to hot gases. The time for the ignition of the trunks is to be determined. Assumptions1Heat conduction in the trunks is one-dimensional since it is long and it has thermal symmetry about the center line. 2The thermal properties of the trunks are constant. 3The heat transfer coefficient is constant and uniform over the entire surface. 4 The Fourier number is τ> 0.2 so that the one-term approximate solutions (or the transient temperature charts) are applicable (this assumption will be verified). PropertiesThe properties of the trunks are given to be k = 0.17 W/m.°C and α= 1.28×10-7m2/s. AnalysisWe treat the trunks of the trees as an infinite cylinder since heat transfer is primarily in the radial direction. Then the Biot number becomes 24.38)CW/m.17.0()m1.0)(C.W/m65(2=°°==khrBioThe constants λ1and A1corresponding to this Biot number are, from Table 4-1, 5989.1and3420.211==AThe Fourier number is 184.0
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