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Rayleigh number and rate of fluid rise due to natural convection in a pipe / duct?

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Old   July 6, 2013, 15:50
Default Rayleigh number and rate of fluid rise due to natural convection in a pipe / duct?
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I have calculated densities for the liquid and solid parts of a substance that has partly melted. The liquid and solid would be at the same temperature.

I would like to do a simple calculation of approximately how long the chocolate would take to rise under natural convection (due to buoyancy). Could anyone please suggest a good way to do this?

I was under the impression that this would be very simple--that I should calculate a Rayeigh number. But after searching extensively online, I realize that I'm very confused. There are various ways to calculate the Rayleigh number and it doesn't actually provide velocity anyway. I guess I would want to use a Rayleigh number for an enclosed duct / cylinder, but I can't find one. I realize this is probably a silly question, but if anyone could point me in the right direction, I would be very grateful.

The reason I want to do all this is that when I change certain conditions under which my density calculations are run, the liquid - solid density contrast changes. So for some conditions, rise should be faster. I want to demonstrate how velocity / rise time can be affected by changing density contrast, when all other parameters remain the same.
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buoyancy, buoyant flow, convection, rayleigh number

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