Are you suggesting that the HEX error is up to 0.26 +20%= 0.31W??? or =+20% of 5W = +1W??.

I am calculating the fractional standard deviation of the measured output power per the simplfied equation given in the prior post. To 'suggest' an actual error I need reliable error estimates on *all* the relevant experimental parameters, which are not available. But that is neither of which you suggest. In fact in my last post I explicitly told you what I was guessing were the noise bands based on a standard error calc. I suggest you re-read my last post.

You wrote B-O-E . What values of ɳ , ΔT , C and ρ are you plugging into your B-O-E?

Doesn't matter. When you use the simplified fractional standard deviation approach, all you need to discuss is the fractional (easily converted to percentage) error of each experimental variable, which were not all given, so I am unable to give a definitive error estimate. I can only approximate from reasonable assumptions, which you may disagree with. But I won't argue about it because the paper's authors were supposed to give them, not make us guess.

For the 80W input energy values Iwamura et al have written error estimates.

oil flowrate error = 0:012(ml/min);oil temperature change error = 0:261(K);

input energy rate error = 0:031(W);

excess heat energy rate error (HEX) = 0:260 (W):

How did they determine these? Since they do NOT seem to know how to do standard error analysis, I have to suspect their given estimates are likewise determined in a non-standard fashion, and thus are effectively meaningless, since I have no idea how to apply them to calculate the standard errors. Usually, for some strange reason, when people determine errors in a non-standard way, they are underestimated. Go figure.

What are your estimates

oil flowrate error = ? (ml/min);

oil temperature change error =? (K);

input energy rate error = ? W);

I did not estimate these numerically. I applied the usual 'sensitivity analysis' approach of examining the impact if the standard deviations were 1, 5 and 10% of the nominal or maximal variable values. That is all that is needed to estimate the fractional standard deviation of the output power. Then I took the 134W reported output power and calculated my estimated noise bands. My conclusion was they are working in the noise, always a bad thing to do if you want to draw definitive conclusions.

The excess power is another calculation, both for the value and for the standard deviation, but they are simple equations that you can figure out easily. Historically, input energy is usually reasonably well measured, as are temperatures (and thereby differences), but flowrate can be a problem in some cases.

excess heat energy rate error (HEX) = ? (W):

Of course that error will be the square root of the sum of the variance in the input and output powers. (There, I told you one of the equations from the answer just above.)

input energy rate error = ? W);

Pin = I * V or Pin = I^2*R . Use the POE equation to answer your question. You will probably have to guess at the errors since we are not informed how the supposed 'delta' is related to the 'sigma', and error calculations use 'sigma' (technically 's', the estimate of sigma).