See below. Most of your questions are answered by a knowledge of basic heat transfer as required by NFPA 1033.

J L Mazerat Wrote:
-------------------------------------------------------
> Wait a minute, uncertainty! Ok let say instead of
> error rate, which is used by the court, we use the
> word uncertainty. The synonyms for uncertainty are
> as follows, distrust, distrustfulness, doubt,
> dubiety, dubitation, mistrust, query, reservation,
> skepticism, and suspicion. Remember the results
> will be presented in court that could be the bases
> for someone going to jail or losing their payments
> from an insurance company. I ask anyone reading
> this to consider is you are the excused would you
> want the trier of fact to accept the results as
> fact.

You are not undertanding the difference between an error rate and uncertainty. In the graph you cited, because of the combined uncertainly in the input variables and the measurement techniques, any data point that falls within the band of uncertainly cannot be said to have any difference between the predicted and actual measurement. Outside of the band of uncertainty, each data point does have a relative error that can be calculated, but that is different than the uncertainty.

>
> Another problem with this not being an error rate
> is that one of the developers of the CFIcalculator
> has testified that the mathematical formula he
> used in determining heat transfer from the source
> of the heat to the target object had a 20-30%
> error rate. Are you saying his testimony was
> incorrect?

There are two correlations depending on the assumptions made. There is a point source model for relatively far distances from the flame radiation source and the solid flame model for near-sources.

Looking at NUREG-1824 will provide you with the answer to your questions about the error rate of these calculations. Radiative heat transfer to a target is very sensitive to the bulk temperature of the flame source. Flames are made up of thing sheets of flame where the oxidizer and fuel diffuse and the combustion reactions occur. There are large temperature gradients across the structure of the flame. What average flame temperature does one use for this equation where the temperature is to the fourth power? In addition, the heat transfer is sensitive to the view factor that is usually an approximation of the actual conditions.

If you look at the relative error for these equations, 20% to 30% error would be a good error rate. Some comparisons are an order of magnitude higher in error rate.

>
> For the test I it is my understanding that the
> data put in was the same for both models and for
> the hand method, yet not one of them agreed with
> the other. This may be because of the formular
> used by each, but then the question is which one
> is correct. These tests did not deal with the
> uncertainly of the input variables and the
> uncertainly associated with the measured
> variables. It may be the way the model and the
> hand method compute the input data and the fact
> that they may use different mathematical
> formulars. I will agree there is an uncertainty as
> to the final results based on these experiments.

The model you use depends on the scenario you are trying to model. The conditions and the model need to be substantially similar. A point source model assumes the target is relatively far enough away for the target to "see" the source as a "point." If the target is relatively close to the source, the height of the flame and geometry now play a role in what the target "sees" as the source.

There is both uncertainty and error associated with these equations that are calculated for you in the NUREG. This is basic heat transfer that falls under the topic of thermodynamics in NFPA 1033, although most undergraduate engineering curriculum provides a separate course in heat transfer. Thermodynamics involves states of energy, where heat transfer provides more transient modes of transport of thermal energy.

Douglas J. Carpenter, MScFPE, CFEI, PE, FSFPE
Vice President & Principal Engineer
Combustion Science & Engineering, Inc.
8940 Old Annapolis Road, Suite L
Columbia, MD 21045
(410) 884-3266
(410) 884-3267 (fax)
www.csefire.com