[time-nuts] Thermal Time Constant

[Bruce Griffiths]

Brooke Clarke wrote:
> Hi:
>
> For some time I've considered surrounding a free running 32678 Hz 
> oscillator (like a Dallas 32khz, or one of the newer Maxim units) with 
> thermal mass and insulation in order to get the time constant into the 
> range of some days.  To get a feel for it a simple experiment shows 
> that a half inch diameter brass rod 3.75" long (102 grams) has a 
> thermal time constant of about 6 min 35 seconds when wrapped lightly 
> in a towel.
>
> Is there a way to calculate the amount of aluminum and Styrofoam 
> needed to get a time constant of say 100 hours?
>
> This came up in relation to WWVB clocks that free run for most of the 
> time.  When you compare WWVB clocks it's not uncommon to see tens of 
> seconds difference between them.  http://www.prc68.com/I/Loop.shtml#TC
>
Start with the maximum thermal resistance the application can withstand 
(determined by internal dissipation and acceptable temperature rise 
above ambient).

If for example the dissipation is 10mW and acceptable temperature rise 
10C then thermal resistance will be about 1000C/W.

The thermal capacity required can then be calculated from the time constant:

C= 3.6E5/1E3 = 360 J/C requires about 7.2 kg of aluminium.

The required thickness of styrofoam can then be calculated from the 
surface area of the aluminium block.

Achieving a thermal resistance of 1000C/W may be a little difficult 
without using radiation shields.

Bruce