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Is there an actual definition of characteristic time? When dealing with heat transfer for instance convective heat transfer between a naked flame and a fluid in a glass bulb, can characteristic time be defined as: the time taken to for the centre of the fluids temperature to be a certain percentage of its surface temperature?

Thanks.

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One commonly used definition is in the case of the solution of Newton's Law of Cooling (or Heating), where one approach uses dimensionless groups.

The solution is, with $\tau$ the characteristic time:

$$\ln\Theta=-\frac{t}{\tau}$$ where: $$\Theta =\frac{T(t)-T_{env}}{T_0-T_{env}}\text{ and } \frac{1}{\tau}=\frac{hA}{mc_p}$$

with:

  • $h$ is the heat transfer coefficient
  • $A$ is the heat transfer surface area
  • $T(t)$ is the temperature of the object's surface, evolving in time $t$
  • $T_{env}$ is the temperature of the environment; i.e. the temperature suitably far from the surface
  • $m$ is object's mass and $c_p$ its specific heat capacity.

Defined that way the characteristic time is:

$$\boxed{\tau=\frac{mc_p}{hA}}$$

can characteristic time be defined as: the time taken to for the centre of the fluids temperature to be a certain percentage of its surface temperature.

No, that's not really how its use is intended.

Reference: A Heat Transfer Textbook (Lienhard & Lienhard)

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  • $\begingroup$ There is some relationship between characteristic time and how close you are to steady state or equilibrium though, isn't there? It's been years since I learned it, but I remember it being similar to the RC time constant which sounds kinda like what OP's teacher was trying to get at. $\endgroup$
    – JMac
    May 13 '20 at 22:36
  • $\begingroup$ Yes, I guess you could make that connection. High CT means slower cooling e.g., so it kind of reflects the cooling time. $\endgroup$
    – Gert
    May 13 '20 at 22:38
  • $\begingroup$ Brilliant guys! I couldnt thank you enough. Im just starting my journey. I hope one day to have the vast knowledge of some people on here. $\endgroup$ May 14 '20 at 8:55
  • $\begingroup$ You're welcome. $\endgroup$
    – Gert
    May 14 '20 at 13:38

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