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Q2:- Carbon steel (AISI 1010) shafts of 0.1-m diameter are heat treated in a gas-fired furnace whose gases are at 1100 K and
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carbon steel ( AISI 2010) properties 7870 kg # density m3 # heat capacitey of carbon steel = 0.502416 J goc =0.502416 KJ Kyoc

c D Le = characteristic length 4 hote 100% 0:1 Biº- K 49.884 Bi Il 0-0502 0.1 Lumped heat capacitly heat capacitly method is

T-TD -HA PVC It a To-To Where T 700 K. = Too Ambient Temp (look) TDF 1100 k Toa initial Temperature To = 300K W be 100 m2k. P

400 In (= cooxt x04 -sor - ( coox € X04 7670 X502-41680:1 t 7870 X502.416X0.1 xhx cois) I olx 100 x 4 = 7 685.178 second 11-4

Time 11.42 minute is required to reach temperature at 700 K from 300K

NB:-. answers may be varies with your answer because of only assumed property of carbon steel .

Please take care of it .

Usually ,this analysis always done by using the lumped parameters analysis because smaller diameter of cylinder and also bio number is less than 0.1 .

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