(Deckwer, 1980)
I'll try to explain this in words:
The (ratio of convection to advection heat transport) is proportional to the negative-fourth root of [(ratio of inertial to viscous forces) times the (ratio of inertial to gravitational forces) times the square of the (ratio of momentum diffusivity to thermal diffusivity)]
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What does that even mean?
It turns out that the above correlation (for heat transfer in a bubble column) can be rewritten as:
(Tow, 2014)
In words:
The (ratio of convection heat transfer to conduction through eddy length) is proportional to the square root of the (ratio of momentum diffusivity to thermal diffusivity).
It works out this way because forced convection is really just conduction through some thermal layer. The keys are just finding out how the thermal layer relates to the momentum layer (in this case, through Pr^[1/2] because of transient conduction interactions with eddies) and finding the size of the momentum layer (in this case, the micro-eddy scale, eta).
