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# time constant-transient heat transfer2

## time constant-transient heat transfer

(OP)
From a plot of temp vs time how can I calculate the time constant? Is that the time when the slope goes to 0 or the temp reaches steady state?
Thanks,

### RE: time constant-transient heat transfer

Perhaps I'm confused about what it is that you are looking for specifically.  For what "time constant" are you searching?

### RE: time constant-transient heat transfer

From my undergrad physics I think there are 2 definitions and it depends on what you are  trying to find out:

1) The thermal time constant tau given by
t = L^2/k    where L is a length and k is thermal diffusivity  tau gives the amount of time it takes for heat pentrate a body to a certain length.

2) Then there is the time contant which measures how long it takes for a body to reach 63% of a specific temp range - so if you submerge an egg at 0C into water of 100C when the centre of the egg reaches 63C thats the time constant for that egg.

But it was all such a long time ago I think my brain has addled.

Why do you want to know and what do you want to know?

### RE: time constant-transient heat transfer

(OP)
Well, sorry I was not clear before. I am running a transient heat transfer on a part where conduction and convection are the primary modes of ht.

If I extend the duration of my sim I can see that my time vs temp plot will approach asymptotic inf. So from one such plot how will I estimate the time constant for the system? (based on my input response)

Hope I am being clear.

### RE: time constant-transient heat transfer

(OP)
I am looking for thermal time constant. I am not sure I understand your equation though. What is this length in the equation?

I am new to HT sims and dont recall this term from my ht classes.

thanks

### RE: time constant-transient heat transfer

sorry typing probably not clear
tau = (length squared)/k
where the length is any length of interest so if we are looking at a sphere and we want to know the time constant of that sphere then length would be the radius of the sphere. The time constant tells us for that sphere how long it takes for heat applied at the surface to pentrate the specified length.

Lets reverse this - what do you define as the time constant and why do you want to find it out? You are looking for the time constant, what is it?

### RE: time constant-transient heat transfer

More apologies, on reflection I the strict definition of the thermal time constant has L as 1 (like 1 metre, or 1mm) which depends on wether you thermal diffsivity is given in mm or m. It varies accros the textbooks on my desk anyway...

### RE: time constant-transient heat transfer

(OP)
You answered my question. I am looking for the thermal time constant which is time taken to reach 63% of the final asymptotic value (steady state temp)

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