ampacity and cooling
ampacity and cooling
(OP)
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!






RE: ampacity and cooling
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RE: ampacity and cooling
RE: ampacity and cooling
RE: ampacity and cooling
RE: ampacity and cooling
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.
RE: ampacity and cooling
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, I2R, to BTUs.
Plug it into the appropriate table, estimate and extrapolate.
Bill
--------------------
"Why not the best?"
Jimmy Carter
RE: ampacity and cooling
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!
RE: ampacity and cooling
ht
In the following thread I tried to explain how to get the formula.
thread238-316320: Fuse I^2t let-through and cable sizing
I don't know the name but you may Google something like "conductor cross section in short-circuit current calculation"
RE: ampacity and cooling
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?