Tempo de Aquecimento de Eixo de Aço AISI 1010: Análise de Convecção e Condução

PROBLEM 515 KNOWN Diameter and radial temperature of AISI 1010 carbon steel shaft Convection coefficient and temperature of furnace gases FIND Time required for shaft centerline to reach a prescribed temperature SCHEMATIC ASSUMPTIONS 1 Onedimensional radial conduction 2 Constant properties PROPERTIES AISI 1010 carbon steel Table A1 T 550 K 7832 kg m3 k 512 WmK c 541 JkgK 121105 m2s ANALYSIS The Biot number is 2 o 100 Wm K 005 m2 hr 2 Bi 00488 k 512 Wm K Hence the lumped capacitance method can be applied From Equation 56 i T T hAs 4h exp t exp t T T Vc cD 2 3 800 1200 4 100 Wm K ln 0811 t 300 1200 7832 kgm 541 Jkg K 01 m t 859 s COMMENTS To check the validity of the foregoing result use the oneterm approximation to the series solution From Equation 552c 2 o 1 1 i T T 400 0444 C exp Fo T T 900 For Bi hrok 00976 Table 51 yields 1 0436 and C1 1024 Hence 2 5 2 2 0436 12 10 m s t ln 0434 0835 005 m t 915 s The results agree to within 6 The lumped capacitance method underestimates the actual time since the response at the centerline lags that at any other location in the shaft