Nanofluid: Dual Core Tests and Review

[relttem]

Ah...the Reynolds Number.

Skinnee sent me a PM about this, and I thought it would be a good thing for all of you to know..for those of you that don't that is. The Reynolds Number, named after Osborne Reynolds, is a non-dimensional number that is very important in fluid dynamics. I am sure Wiki has a good write up about it, so I won't go into the details of it. In heat transfer you have a few non-dimensional numbers that you commonly use with the Nusselt number probably being the most common. The Nusselt number, Nu, is related to the Reynolds Number, Re by the equation:
Nu = X*Re^y*Pr^z

Pr = prandtl number
X, y, z = constants depending on fluid and flow.

In the paper I have been sending out, we were using the LOCAL Reynolds number. This is a measure of the Re at a specific location. The equation for Re is:

Re = (rho*V*D)/mu

rho - density
V - velocity
D - diameter
mu - viscosity

also,

Re = (4*mdot)/(mu*pi*D)
mdot - mass flow rate

You have to make sure you are using the same system of units - all your units should cancel out. Thus, the non-dimensional. There is a good website, onlineconversion.com that will let you change gpm to kg/s etc.

local Re is

Rex = (rho*V*X)/mu

X is the distance you are measuring the Re

So, if you wanted to compute the Re of your system you need to know a few things, and then crunch through some equations. First you have to know the gpm your pump puts out. Then, go to onlineconversion.com and convert that to kg/s. Next you have to know the diameter of your tube..preferably in meters...you can use the same website to convert inches to meters if you are unsure of how to do it. Now, you can get your Re using the equation above. You'll have to find the dynamic viscosity and density for water at your systems temp, but you can get that online. With those numbers you can get a very close estimate of the fluid velocity using

mdot = rho*V*A
A - area (pi*D^2)/4

solve that for V

Those are the V and Re for your Tube. Now, you have to move to your water block. You would have to know the dimensions of the flow channels in the water block, and if there is branching flow etc to accurately calculate the Re. It gets a little tricky, but you can make some general assumptions and get a reasonable estimate of your Re in the block. Knowing the Re you can use the graphs to get an estimate of the convective coefficient, h. Then, you can determine how much heat is being removed using

Q=h*A*(T2-T1)

That will give you a ballpark number since there is a lot more going on that just that.

thanks...I will be here all week.