Rate of Heat Lost 1

[SolDirJoe]

Can any one offer best formula [with definitions and units] to calculate the heats lost by hot copper wire as it transits through a coolant at high speed. ?

ie. Wire T 400 deg C : Coolant 15 deg C : speed 30 metres per second.

 

[EngineerBSME]

What is the coolant media for the copper wire?
Liquid of gas
water or air
Conduction, convection, and radiation are the three means of heat transfer. Each must be addressed separately.

 

[SolDirJoe]

The coolant is water constantly recirculating from a reservoir into a tank at a high flow rate through which the 0.50mm diameter wire is travelling at 30 m/sec. The "tank" dimensions are 600mm long : 350mm wide : 150mm deep. The temperature of the wire on entry is 400 deg C. Coolant temperature constant at 15 deg C

 

[quark]

SDJ!

The amount of heat to be removed from the copper wire comes from the formula Q1 = mCp(T2-T1) (and I am assuming you are cooling down copper wire to ambient temperature)

m = mass flow rate of copper = [3.142x(dia.)²xfeed rate(30m/s)xdensity]/4
= 3.142x0.0005²x30x8920/4 = 0.053kg/s
(dia. of the wire is in meters and density is in kg/cu.m)

Cp = specific heat of copper is 400 j/kg deg.C

Therefore Q = 0.053 kg/s x 400J/kg deg.C x (400-30)deg.C
= 7844 j/s = 7.844 kW (or 1867 cal/s = 6721 kCal/hr)

When I check water side the temperature rise seems to be very very less.

Now I check what is the conduction rate of copper wire by the formula Q2 = KA (T2-T1)/t
where k = conductivity of copper = 370 W/mK
t = thickness of copper wire = 0.0005 M
T2 = temperature of copper wire = 400 deg.C
T1 = temperature of cooling water = 15 deg.C
A = contact area of copper wire with water = 3.142 x D x L
if I consider the wire is being fed length wise then the length of copper wire is length of tub = 0.6 M

so A = 3.142 x 0.0005 x 0.6 = 0.00094 Sq.M
Q2 = 370 x 0.00094 x (400-15)/0.0005 = 267.8 kW

As Q2 is far larger than Q1 there is no problem with heat transfer.
So total heat rejection by copper wire = Q1 = 7.844 kW

To maintain this even 2 liters/sec water flow is sufficient.

Note: Better post heat transfer problems in Heat Transfer&Themodynamics Engineering Forum.

Regards,

 

[pmover]

i believe this is a transient conduction problem to be solved by the lumped capacitance method (that is Biot number and Fourier number).

I understand the problem that the wire is passing through a tank of water at 30m/s. the tank dimensions are given as is the coolant and wire temps. Please confirm.

by inspection, the wire is exposed to the water for a short period of time (i.e. < 0.2 secs).

One would need to determine the heat transfer coefficient, h from the nusselt number.

is the copper pure copper or a fraction thereof?

once h is determined, then the temperature of the wire leaving the tank can be determined, thus so can the heat transfer rate.

i would neglect radiation effects and assume the water in the tank is maintained at a constant temperature by some other means.
-pmover

 

[quark]

Pmover!

I don't think the heat transfer is transient. The temperature of copper wire, temperature of cooling water, speed of copper wire and velocity of water all are constant and at any moment of time same quantity of heat gets transfered from the wire to water. That is why I considered steady state condition.

 

[pmover]

ok,
i understand the problem that the 0.5mm copper wire, at 400oC & at 30m/s through the coolant, is passing through a 15oC (constant) water coolant bath tank of size 650mm x 350mm x 150mm.

I doubt that any point along the copper wire is cooled to 15oC in the time it passes through the coolant (i.e. < 0.2 secs).

hence my reasoning for a transient problem.

perhaps the originator can elaborate and/or clarify the problem.

-pmover

 

[poetix99]

400 deg.C is rather hot! Last time I checked my steam tables, water boiled at 100deg.C.

I mention this because there will be a (small) &quot;jacket&quot; of vapor around the wire, at least at the inlet side of the coolant tank. Considerably lower h.t. coefficient if it is effectively insulated for a period of time.

Also, remember the total residence in the tank is
0.65m/30(m/s) = 0.022 sec.

Is any air, even the smallest amount, entrained on the wire as it flies into the coolant tank. Yes, it is. Down goes the h.t. coeff. again.

If it weren't for the phase change of the water, I would intuitively line up with &quot;quark&quot;, but there is too much going on for me to be very comfortable with that kind of bulk analysis in this case.

I think that a lumped parameters analysis could also easily get into errors of oversimplification of the convective film coefficent.

Calculating a few values of Biot number will validate/invalidate &quot;quarks&quot; analysis; IF you think you know &quot;h&quot;.

I'm just too tired, or lazy, or unimaginative to do it.

 

[quark]

Pmover and Poetix!

I too agree that I should verify the convective heat transfer. My above posts nowhere mention contrary to this.

There are two reasons for why I didn't check that. I will say it eventhough it is untechnical to say it.

1. I am lazy to further prolongate my first post.
2. I had a feeling that the original poster was talking about an existing process. (and I thought I have to only check heat lost from the wire)

I by no means defending my post here (if it is wrong, it is wrong)

Thanks for you guys to take effort in perfecting the solution.

Cheers!

 

[pmover]

quark,

thank you for the confirmation.

the important parameter in this problem is the convective heat transfer coefficient. determine that parameter and the outlet temperature can be determined; thus, so can the heat rate removal from the wire as it transits the coolant.

one would need to determine reynolds # and Nusselt number for this situation (I cannot find in my heat xfer textbook reference to flow parallel to a cylinder for Re# and Nud#) or one would need to investigate nucleate boiling since the copper wire temp is well above the boiling point of water.

-pmover

 

[quark]

pmover!

I long back checked the parameters of nucleate boiling but the heat flux coming out to be quite huge(of the order 10¹³watts/sq.m - perhaps you can have a check). However there is some data given for platinum wire in Heat Transfer by Holman and I found no problem with our case.

As for transient conduction, I totally disagree because the diameter of the wire is very smallblems and I saw no problems dealt with moving cylinders. (even the Biot number is coming out to be lower (approximately 1/100 times to the limiting value)

For better convection water should pass across the wire so that even temperature cold water comes into contact with the whole length of the wire.

However I would anticipate original poster to interfere at this juncture for I can't assume anything further

Note: My gut feeling is there should not be any problem.

Cheers

 

[SolDirJoe]

Thanks guys,
All very helpful stuff. To answer few queries :-

Cu is 99% pure. The wire is electricaly heated as it passes through a nitrogen atmosphere [to prevent oxidation], before passing into the coolant chamber. Transfer from one chamber to the other is via a grouve in a rotating brass cylinder [also serving as an electrical connection to the low voltage, high current heating power source].

Coolant is pumped at high flow rate into the cooling, or quench chamber and recirculated via heat exchanger to maintain temp at 15 deg C.

In effect the transition from hot to cold can be considered instantaneous, with the wire passing through turbulent coolant in 20 mSec.

My own [less educated] calcs give an exit figure of 22 deg C, but I have no confidence in them. Wire speed too fast for T/Couple or I/Red thermal imaging equimpent but I need to find better method of achieving consistent quality of copper wire.

Thanks for the excellent data

SolDirJoe

 

[pmover]

quark,

after some reading last night, i'll now agree that my previous post is likely not the appropriate technique to solve the problem (that is biot and fourier number, etc.).

interestingly, the textbook (Incropera and deWitt) provided 3 definitions of nucleate boiling, with one addressing situations when the temperature difference between the surface temperature (this case copper wire) and the saturated temperature (this case water) is > 120degF.

again, once the heat transfer coefficient, h is determined, the rest can be solved.
-pmover