Forced convection of a copper sphere

[mogui]

Hi, I'm having a difficult time with what should be a simple problem:
I'm trying to find a fluid velocity using a cooling rate of a copper sphere following a lumped capacity model. I have all the correct units and thermodynamic properties; and I believe I have all the correct equations. I keep getting very wrong answers that are less than one and almost the same for all agitation speeds.
The sphere contains a heater and type K thermocouples. The temperature is allowed to reach a steady state with water agitation, after a set amount of time the heater is turned off and the cooling is monitored in 10 second intervals. This process is repeated for different agitator speeds. I know what the flows should be for the small tank, and I need to be able to calculate them so I can find velocities for the large tank. Here's the equation I've been using:

Nu=2+(0.4*Re^(.5)+0.06*Re^(2/3))*Pr^(.4)*(u/us)^.25

Can someone help? I don't know if the experiment or my calculations are way off.

 

[Onno]

Some guidelines. From the Nu(sselt number you will calculate the heat exchange coefficient.

free conv. 1-10 watt/m^2*K
forced conv. : 10 - 100 watt/m^2

I suppose you know the Re numbers? <2400 laminar, above turbulent.

I ask you to find the average, typical value for Pr(andtl) you might expect. In short, get a feeling first for the order of magnitude your different equation variables have.

 

[mogui]

Because the fluid velocity is the unknown I'm looking for, I've been using Pr and Nu to find Re with excel solver. The heat transfer coefficient I've been comming up with has been between 50 and 100,000. My Pr has been about 6.36, which is reasonable, but Nu has been all over the place. Re tends to be in the 2450-4800 range.

 

[Onno]

Consider the following line of reasoning.

Excel is a program that possibly can give you answers. However these answers are primarily mathematical by nature. The solver only looks for numbers that fit the equation.

Back to your problem now. You probably have a pump that is used to create a flow of cooling medium around the sphere. You know the capacity of this pump to move things so this is your entrance to the problem. From here you start, from the possibility in your system to move the cooling flow.

Then you calculate the time-temperature for he cooling of the sphere since all variables in the equation are known.