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Why Reynolds Analogy and other empirical relations always overesimate heat transfer?

I have done an experiment on turbulent pipe flow (smooth pipe) and I used Reynold Analogy (both the simple (Pr=1) and the modified one) and the Dittus-Boetler correlation equation to do the predictions.

It turns out that all those predictions over-estimate the heat transfer i.e. the Nusselt number at each Reynolds number.

I can't figure out why...

Is that there are some kind of energy or heat loss not considered? (There is some lagging material around the pipe and the loss through the laggin materials has been measured)

Please share your views. Thanks.

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# Why Reynolds Analogy and other empirical relations always overesimate heat transfer?

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