I worked for a NRTL for years, and no reviewer worth his salt ever accepted an 
equation for thermal time constant or steady-state temperature.  Just the data, 
Ma'am.... Brian Gregory720-450-4933

---------- Original Message ----------
From: Doug Powell <doug...@gmail.com>
To: EMC-PSTC@LISTSERV.IEEE.ORG
Subject: Re: [PSES] Thermal equilibrium - 10% rule
Date: Sun, 8 Jan 2017 11:38:30 -0700


Richard, I have tried a number of approaches in the past.  Given that most 
products are quite complex with regard to all the potential heat sources/sinks 
and interfaces I decided that anything along the lines of FEA is impractical.   
I also tried the time constants idea which is analogous to RC time constants.  
I found this works well enough if you have a good amount of history with the 
product itself.  Otherwise, due to the non-linear nature of the problem, it is 
difficult to predict end time or temperature until 3 to 4 time constants have 
already passed. I tried using the slope of &Delta;T to estimate when the end of 
the test is pending. The next attempt was to dig in a little following the 
equations V = Voe-(t/RC) and V = Vo[1-e-(t/RC)] where I substitute V for the 
the various temperatures (Vo = the absolute value of the temperature delta from 
start to end), C is analogous to product mass and R is the Rtheta of the 
product. With a little testing history, you can assume the composition of the 
product is similar for other products designed by the same company (copper, 
steel, plastics, air, liquids, etc), I solved for RC and then rearranged the 
algebra to solve for t which is time.  There are a couple of problems in that I 
am still unable to come up with a general purpose solution.  First this is a 
simultaneous solution of several unknowns which is not conducive to quick on 
the fly solutions.  This is especially true when you are in the early stages of 
a temperature run when things are still moving quickly.  As you know 
extrapolating outside an existing dataset is risky, especially when 
nonlinearities are involved.   I am now going back to basics.  Q = Cp * m * 
abs(T2-T1) q = heat energy in Joulesm = mass of the productCp = specific heat 
of the productT1 = The initial temperature of the product at the startT2 = The 
final temperature of the productabs() is used to correct for heating or cooling 
With the start/final temperatures and mass taken from prior tests I can extract 
a Cp for a particular product. Understanding one watt is Joules/second you can 
factor into the equation time.    My thought is that the composition of a 
product from the same engineering group with have similar ratios of copper, 
iron, plastics, etc.  And then I may be able to solve for total test time or 
final temperature.  Not forgetting that the air mass and equipment of the 
environmental chamber is part of the big picture. I have not fully tested this 
method yet, but so far I remain hopeful.  If this works, I plan to build a 
small database of product Cp values.  I would be interested to know if anyone 
else gives this a go and how as yet undiscovered problems are overcome.  -Doug 
Douglas E PowellLaporte, Colorado 
USAdougp01@gmail.comhttp://www.linkedin.com/in/dougp01       
On Sat, Jan 7, 2017 at 12:51 PM, Richard Nute <ri...@ieee.org> wrote:
> We have to consider that the temperatures sought are not of
 > metrological value, but to
 > to establish a safe/non-safe result.
 
 Yes!
 
 > The mathematical limit of an exponential rise is easy to
 > estimate, once a few timed samples are available,
 
 I haven't been able to come up with an equation, even though I have tried and 
sought help from folks who are more knowledgeable than me in the field of 
thermodynamics.  Please tell us your methodology.
 
 Best wishes for the New Year!
 Rich
 
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doug...@gmail.com
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