[time-nuts] Thermal Time Constant

[Bruce Griffiths]

Surely you meant 1 square inch of styrofoam with the specified thickness??

For a 100 hour (3.6E5 seconds) time constant and 1000 deg C/W thermal 
resistance you need a thermal capacitance of 3.6E5/1E3 = 360 J/C
or 360/0.8371 = 430 gm of Aluminium which has a volume of 430/2.7 = 159 cc.

You still have the thermal radiation coupling problem through the 
infrared transparent insulator.
Gold plating the aluminium will help.

Even if you solve the thermal radiation problem, the thermal conductance 
of any leads bringing power or signals to or from the clock will be an 
major problem even if you use constantan or austenetic stainless steel 
leads.

Bruce

Brooke Clarke wrote:
> Hi Bruce:
>
> If a square meter of Styrofoam is 1.5 deg C/W then a cubic  inch would 
> be 39.37 * 39.37 * 1.5 or 2,325 deg C/W
>
> The DS3231 dissipates about 1 mw when running.  I'm not sure how to 
> come up with an allowable temp increase, but suspect it's based on not 
> exceeding the max allowed operating temp.  But for this part the Temp 
> vs. freq curve is flattest at room temp so best to minimize the temp 
> rise.
> So:  (1 deg C) / (0.001 W) = 1000 deg C/W, the same number you had.
>
> That requires 185 g of Aluminum or about 69 cc volume or 4.25 cubic 
> inches.  That's a block about 1.62" on a side.
>
> How does that look?
>
> Have Fun,
>
> Brooke Clarke
> http://www.PRC68.com
>
>
> Bruce Griffiths wrote:
>> Thermal resistance is measured in degrees (C or K or ..) per watt.
>> Its inversely proportional to area and proportional to thickness.
>>
>> I think the clueless clown who created that table means that for a 1 
>> square meter panel of the specified thickness the thermal resistance 
>> is the tabulated value measured in Kelvin/Watt.
>>
>> Bruce
>>
>> Brooke Clarke wrote:
>>> 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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>>>
>>>
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