Chapter 4 Transient Heat Conduction4-38A long cylindrical shaft at 400°C is allowed to cool slowly. The center temperature and the heat transfer per unit length of the cylinder are to be determined. Assumptions1Heat conduction in the shaft is one-dimensional since it is long and it has thermal symmetry about the center line. 2The thermal properties of the shaft 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 stainless steel 304 at room temperature are given to be k = 14.9 W/m.°C, ρ= 7900 kg/m3, Cp= 477 J/kg.°C, α= 3.95×10-6m2/s AnalysisFirst the Biot number is calculated to be 705.0)CW/m.9.14()m175.0)(C.W/m60(2=°°==khrBioSteel shaft Ti= 400°C Air T∞= 150°C The constants λ1and A1corresponding to this Biot number are, from Table 4-1, 111093511558==..and AThe Fourier number is 1548.0m)175.0(s)60/s)(20m1095.3(2262=××==−Ltατwhich is very close to the value of 0.2. Therefore, the one-term approximate solution (or the transient
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This note was uploaded on 01/19/2012 for the course PHY 4803 taught by Professor Dr.danielarenas during the Fall '10 term at UNF.