
#1
Apr2113, 10:50 PM

P: 248

16. As part of a heattreating process, an alloysteel billet, initially at 1032°F, is cooled in a 32°F air stream. The temperature history of the billet is shown in the figure at right.
What is the time constant τ for the cooling process? I have attached an image of the question. I have the equation: T = T_{∞} + (T_{i}T_{∞})e^{t/τ} I know that: T_{∞} = 32°F T_{i} = 1023°F But I'm a little uncertain about the time. If I take the max temperature value, 1032°F, and multiply this by 0.368, would this give me the time and temperature at one time constant? 



#2
Apr2213, 02:01 AM

HW Helper
P: 4,716

Exponential decay is based on the difference value, the difference between where it is now and where it is headed finally. In one time constant it closes the distance by 63.2% leaving 36.8% of that difference to go.



Register to reply 
Related Discussions  
Cooling Time of Steel Block  Mechanical Engineering  5  
Approx. time universe had cooled down for a particle...  Introductory Physics Homework  0  
About fieldcooled / zerofieldcooled curves of superparamagnetic particles?  Atomic, Solid State, Comp. Physics  1  
Time to Freeze Standing Water in Steel Pipe  Mechanical Engineering  13  
Model to predict time needed to cool down steel billets.  General Engineering  6 