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

Question

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.

Answer 1

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)