dependence heat loss on speed

[McCrunchy]

Hello all,

 

I have a slightly technical question.

I'm trying to solve a problem on a stream (vertical jet) of hot water cooling in air (think of pooring tea). I want to compute the temperature of the water as it goes down. Now, since the water is accelerating (free fall), the speed of the jet is different in different places, and so is the heat loss. However, I do not know the dependence of heat loss on speed. Assuming the flow of air next to the stream is non-turbulent, I tried solving the heat equation, but with only one boundary condition (the stream/air interface), I spinned my wheels a bit and gave up.

 

Is there a reference on this dependence ? It must be a classical pipe-type heat transfer problem.

 

Thanks,

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Merged post follows:

Consecutive posts merged

and disregarding the dependance of heat loss on speed, but rather taking the wikipedia value of still air's thermal coefficient, I get that a 30 cm long, 1 mm in radius stream of boiling water gets cooler by 1°C. I'd be curious to see by how much taking into account the speed of the jet would increase this value ...

 

 

McCrunch