ampacity and cooling 1

[autonub]

Hello! I'm having a little difficulty figuring out how to calculate the maximum ampacity of a metal submerged in water with a constant temperature and flow rate. For example, say we have an aluminum cylinder (solid and without insulation) submerged in water flowing at 30 gallons per minute at a temperature of 45 degrees Celsius. The aluminum has an ampacity in air of 700A per square inch. In the event cross sectional areas and lengths are needed, assume its cross sectional area is 0.5 inches squared and its length is 8.75 inches. Alternatively you can make up your own numbers. I only need to see an example. Thanks!

 

[jraef]

So you are planning on using the aluminum tube as a conductor and it has water flowing through it?

"Dear future generations: Please accept our apologies. We were rolling drunk on petroleum."
— Kilgore Trout (via Kurt Vonnegut)
For the best use of Eng-Tips, please click here -> faq731-376

 

[autonub]

No, not a tube. And no, not flowing through it. The aluminum conductor is essentially a solid rod. The water is flowing around it as if the rod were submerged. The actual scenario is a little more complicated but for our purposes let's assume uniformity in exposure to water. If it helps to invision it, imagine it being a single strand wire a half an inch in diameter, submerged at the center most point in a river with a constant temperature and flow rate.

 

[davidbeach]

And how do you keep that water sufficiently non-conductive?

 

[autonub]

I'm not sure that is crucial to the original question of cooling and ampacity (maximum current carrying capacity). But for the sake of simplicity, let's just assume the water is distilled (pure water). Let's also assume the nearest path to ground through the water is of near infinite resistance, thus any undesirable shorts are completely and utterly negligible; until the conductor (aluminum rod) reaches its melting point.

 

[7anoter4]

It is an interesting issue, indeed.
I have nevertheless some questions.
The current will be constant?
The time up to the maximum temperature reaching will be short-time [0-2 sec.] or hours?
The water flows along the cylinder, I think.
If it is short time the phenomenon is almost adiabatic so the water does not play any function.
From IEEE-80/2000 form.37
I=Amm^2*SQRT(TCAP/time/alpha/ro/10^4*ln((Tf+Ko)/(Ti+Ko)))
alpha=0.00403
ro=2.86
alpha=0.00403 TCAP=2.56
ro=2.86 Ko=228
If the phenomenon duration will be long but still not infinite
Pinput*time=Qtemp.raise+Poutput*time
Pinput= I^2*Ro*(1+alpha*(T-To))
NOTE: alpha is defined only for 0-100 dgr.C for 700 dgr. Will be less. The formula could contain more terms relevant for an elevated temperature.
Poutput=Pconv+Prad+Pcond.
Pconv depends on water properties
Pconv=h*surf.area*(T-Ta)
h=Nu*k/D
Nu=Nusselt factor k=water thermal conductivity D=AL cylinder diameter.
Nu=C*Re^m*Pr^(1/3)
For an isothermal long horizontal cylinder, as Hilper suggests.
See:

http://www.me.uprm.edu/o_meza/Inme4032/Natural

and Forced Convection Experiments-2.doc
Re=Reynolds number
Re=w*D/niu
w=water speed [2-3 m/sec ???] niu=cinematic viscozity [for water 40 dgr.C=0.66/10^6 m^2/sec]
Pr= Prandtl number [for water 40 dgrC=4.35]
Prad=eps*sigma*(Tf^4-Ta^4)
eps[for oxided AL]=0.1-0.2 sigma=Stefan-Boltzmann constant for black body.
Tf and Ta in Kelvin dgr.
Pcond may be neglected for fluids.
Qraise.temp=Tcap*Vol*(Tf-Ti)
Vol=cylinder volume
Tcap=thermal capacity of AL [2.6 J/cm^3/dgr.C]
The calculation normally include an integration but an average calculation could be enough.

 

[waross]

Is this homework??
Find a program for designing keel coolers. (Google?) I had such a program years ago, haven't seen it for some time.
Convert the heat developed in the conductor, I[sup]2[/sup]R, to BTUs.
Plug it into the appropriate table, estimate and extrapolate.

Bill
--------------------
"Why not the best?"
Jimmy Carter

 

[autonub]

waross: No, this is not a homework assignment. It is (sort of) an actual work assignment. The scenario isn't real, but the underlying principles are the same. In other words, if I figure out the solution to the questions I've asked in this thread, I'll in theory be able to solve the real problem at work. I can't be more specific about the real scenario due to the sensitive nature of my work.

7anoter4: Thanks for the great reply! The current is constant DC. Does the first equation you mentioned have a unique name? I'd like to google it. Unfortunately, I don't have IEEE 80-2000 and can't afford to buy it.

Thanks again!

 

[7anoter4]

Kerate -well-known cable manufacturer-gives a simplified version:

http://www.kerite.com/catalog/catalogfiles/short_circuit_limitations.htm

In the following thread I tried to explain how to get the formula.
thread238-316320
I don't know the name but you may Google something like "conductor cross section in short-circuit current calculation"

 

[tinfoil]

Mechanical engineers have a whole specialty devoted to working out oil and gas-fired boiler tube heat transfer rates and temps.

From the water's POV, it doesn't care what made the aluminum tube 'hot'. Boiler heat-transfer equations and concepts can be used for that half of your problem.

The aluminum tube with a DC current should have near uniform current density (no skin effect), so you should be able to easily calculate the core and surface temperatures for a given heat generation/transfer rate (based on constant current and Ohm's law)

Choose a maximum acceptable Al temperature (depends on grade/alloy of metal and whose standard you are reviewing (you may not care about loss of mechanical strength through annealing so you can accpet a higher temp).

Assume steady-sate conditions. Solve your simultaeous equations.

But how do you plan to maintain electrolyte-free water and avoid aluminum oxide production at higher temperatures?