# [time-nuts] Thermal Time Constant

Brooke Clarke brooke at pacific.net
Wed Mar 10 19:36:54 UTC 2010

```Hi Bruce:

What does m2K/W mean?  See:
http://building.dow.com/europe/uk/proddata/styrofoam/thermal.htm

50 mm it's about 1.5 and for 100 mm it's about 3.

Have Fun,

Brooke Clarke
http://www.PRC68.com

Bruce Griffiths wrote:
> Bruce Griffiths wrote:
>> 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
>>
>>
> Oops, the specific heat of Alum9inium is about 0.2Cal/gm/C or 0.8371
> J/gm/C so the mass of Aluminium required would be 430gm if the thermal
> resistance to ambient were 1000K/W. With a thermal resistance of
> 100C/W you need 4.3Kg of aluminium ....
>
> Bruce
>
>
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```