Forced convection at high Prandtl number in laminar flow for a sphere

[Gabriel89567]

thread391-131254

Hello everyone,
I am having quite the same problem as the one exposed in thread391-131254, that is to say I need to have a correct correlation for the convection constant on a sphere in a fluid flow. In short, it is to measure indirectly the fluid's average speed: I go back from the thermal heating profile to the correct value of Reynold's number.
My flow is laminar with Reynolds being between 20 and 400, but my Prandtl number is about 1000 since I am working with engine oil. This is ways beyond the limit for using Whitaker's correlation, which is the one referenced in the previous post ( Prandtl's max would be 380). So I am loking for another correlation at higher Prandtl values.
Does anyone have an idea? My sphere's size is about 1 centimeter

Thanks for your help

Gabriel

 

[ione]

You could try Hughmark correlation for Pr>250 and 17<Re<450

Nu = 2 + 0.4*Re^(1/2)*Pr^(1/3)

Well take it for what it is, namely a best-fit for experimental data (dated back 1967)

 

[Gabriel89567]

Well... Thank you sincerely for your attention, your correlation yields mind-boggling results in my case, namely a very low convection constant. It lacks two terms that were in the previous correlation (Whitakker): 0.4*Reynolds^0.5 + 0.06*Reynolds^0.667 and a factor volumic mass of liquid/volumic mass of water. I think Hughmark meant his correlation for experiments in water only, didn't he? This would explain the lack of the second factor. As for the first one, he is indeed negligible at low Reynolds number.

 

[Gabriel89567]

Sorry, the multiplicative factor is (viscosity of liquid/viscosity of water)^0.25

 

[EnergyMix]

Gabriel, Something is not coming through on your posts. Are you crossing out the data or is that supposed to be an underline?

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[Gabriel89567]

I cross the terms that miss in Hughmark's correlation

 

[dvd]

Is it possible to gather experimental data?

 

[Gabriel89567]

Dvd, yes it is, but I haven't really got the time... I won't spend more than two more weeks on this project so I need to focus, but indeed it would be interesting. I'll think about it; The Gabriel-dvd experimental best fit for laminar-flow forced convection around a sphere at high Prandtl number!