# What could a definition of characteristic time be when dealing with heat transfer?

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.

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)

• 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.
– JMac
May 13 '20 at 22:36
• Yes, I guess you could make that connection. High CT means slower cooling e.g., so it kind of reflects the cooling time.
– Gert
May 13 '20 at 22:38
• 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. May 14 '20 at 8:55
• You're welcome.
– Gert
May 14 '20 at 13:38