Thermodynamics HW Solutions 312

Thermodynamics HW Solutions 312 - Chapter 4 Transient Heat...

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Chapter 4 Transient Heat Conduction 4-38 A 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. Assumptions 1 Heat conduction in the shaft is one-dimensional since it is long and it has thermal symmetry about the center line. 2 The thermal properties of the shaft are constant. 3 The 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). Properties The properties of stainless steel 304 at room temperature are given to be k = 14.9 W/m. ° C, ρ = 7900 kg/m 3 , C p = 477 J/kg. ° C, α = 3.95 × 10 -6 m 2 /s Analysis First the Biot number is calculated to be 705 . 0 ) C W/m. 9 . 14 ( ) m 175 . 0 )( C . W/m 60 ( 2 = ° ° = = k hr Bi o Steel shaft T i = 400 ° C Air T = 150 ° C The constants λ 1 and A 1 corresponding to this Biot number are, from Table 4-1, 11 10935 11558 == .. and A The Fourier number is 1548 . 0 m) 175 . 0 ( s) 60 /s)(20 m 10 95 . 3 ( 2 2 6 2 = × × = = L t α τ which 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.

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