Tratamento Térmico de Rolamentos de Aço Inoxidável - Cálculo de Tempo e Carga Térmica

PROBLEM 567 KNOWN Diameter and initial temperature of roller bearings Temperature of oil bath and convection coefficient Final centerline temperature Number of bearings processed per hour FIND Time required to reach centerline temperature Cooling load SCHEMATIC L 1 m Stainless steel N 10 D 010 m T C i o 500 T0t 50 C f o Oil bath h 500 Wm K 2 T 30oC oo ASSUMPTIONS 1 Onedimensional radial conduction in rod 2 Constant properties PROPERTIES Table A1 St St 304 T 548K 7900 kgm3 k 190 WmK cp 546 JkgK 440 106 m2s ANALYSIS With Bi h ro2k 0658 the lumped capacitance method can not be used From the oneterm approximation of Eq 552c for the centerline temperature 2 2 o o 1 1 i T T 50 30 00426 C exp Fo 11382exp 09287 Fo T T 500 30 where for Bi hrok 1316 C1 12486 and 1 13643 from Table 51 Fo n 00341 186 182 2 2 6 f o t For 182 005m 440 10 1031s 17min From Eqs 547 and 554 the energy extracted from a single rod is o i 1 1 1 2 Q cV T T 1 J With J1 13643 0535 from Table B4 2 3 7 00852 0535 Q 7900kg m 546J kg K 005m 1m 470K 1 154 10 J 13643 The nominal cooling load is 7 5 f NQ 10 154 10 J q 149 10 W 149 kW t 1031s COMMENTS For a centerline temperature of 50C Eq 552b yields a surface temperature of o i o o 1 T r t T T T J 30 C 470 C 00426 0586 417 C