Characteristic timescale of a can of beer? Modelling a 440 ml can of beer by Newton's law of cooling, the temperature difference between the can and its surroundings (e.g. a fridge) decays exponentially in time at a rate determined by the e-folding time or "characteristic timescale".
Ideally, this characteristic timescale would be determined by experimentation to give the best approximation for a particular environment (fridge). In the absence of necessary equipment to perform the experiment, can the characteristic timescale be estimated to reasonable accuracy from first principles?
 A: 
Modelling a 440 ml can of beer by Newton's law of cooling, the
temperature difference between the can and its surroundings (e.g. a
fridge) decays exponentially in time at a rate determined by the
e-folding time or "characteristic timescale".

It's worth noting that Newton's Law of Cooling is essentially an approximation in which internal conduction is assumed to be absent and the temperature of the object is uniform at all times.
The Law states:
$$\dot{\mathrm{q}}=hA[T(t)-T_{\infty}]$$
where $T_{\infty}$ is the environment's (assumed constant) temperature and $T_0$ the initial temperature of the object.
Developed:
$$-mc_p\frac{\mathrm{d}T(t)}{\mathrm{d}t}=hA[T(t)-T_{\infty}]$$
This ODE is separable and on integration yields:
$$\ln\Big[\frac{T(t)-T_{\infty}}{T_0-T_{\infty}}\Big]=-\frac{t}{\tau}$$
with:
$$\tau=\frac{mc_p}{hA}$$
where $1/\tau$ is the characteristic time.
Sometimes, the dimensionless group:
$$\frac{T(t)-T_{\infty}}{T_0-T_{\infty}}$$
is referred to as the reduced temperature $\Theta$, so we get:
$$\ln\Theta=-\frac{t}{\tau}$$
Or:
$$\Theta=\exp{(-t/\tau)}$$
In $\tau$, $m$, $c_p$ and $A$ are usually accurately known. But $h$, the convective heat transfer coefficient (aka the 'film coefficient') is not as straightforward to determine.
The determination of $h$ can be made empirically, from specialist tables or from theory.
The convective heat transfer coefficient $h$ can be calculated from the dimensionless number $\mathrm{Nu}$, the Nusselt number as follows:
$$h=\frac{\mathrm{Nu}k}{L}$$
where $k$ is the thermal conductivity and $L$ a characteristic length.
For some more information on this topic, see this page e.g.
There's also this excellent ebook on Heat Transfer that goes into great detail regarding the 'film coefficient'. See Ch.3, p.269.
A: No, because this timescale is dependent on the material inside and outside the can.
The can will lose heat to the environment by radiation and conduction from its surface.  The rate at which this occurs is dependent on the colour of the surface (dark surfaces are more effective radiators) and the rate at which heat is transferred from the body of the can to the surface. In the case of a real can, the outside edges will start to cool first, which will set up convection currents within the beer, transferring heat from the interior to the surface.
Finally the effects of the air in conducting and convecting heat away from the can need to be considered.
For the case of a spherical perfectly black body in a vacuum with perfect interior heat conduction, the rate of heat loss can be calculated. For real cans of beer, an empirical approach is best.  (45 minutes is enough to chill most drinks to close to fridge temperatures https://www.omnicalculator.com/food/chilled-drink)
