Calculate the rise in temp in copper 3 core wire

[Anugya]

Dear Guys,

It will be really helpful if some one can give me the calculation step by step or some calculator where in I can resolve my long pending problem. Thanks in advance I will be really glad to have a correct answer. The Q is below

Calculate temperature rise in 3 core cable after 3 hrs. resistance 2.74 ohms/km at 20c . Ambient temperature is 33.4c . Length of cable is 140 meter and current passing through cable is 24.97amp this is three phase connection so I will be= 24.97/1.732. Size of each core is 6.30 sqmm density of copper 8.89. So weight of copper in 3 core cable 140 meter comes to: 23.52kg copper.

 

[Nidum]

I don't understand the purpose of this question . Normally you can select cable which is safe for any power requirement just by consulting manufacturers data .

To actually calculate the temperature rise is going to be problematic anyway - there are just too many unknowns in problem as stated .

If you can tell us why you want to estimate this temperature and give us some background to the problem you may get a better answer .

 

[Hesch]

#1: You must know the thermal resistance as for the cable , e.g.: [ ( °C * m ) / W ].

Also you must know the specific heat capacity as for copper and isolation material.

Now, say that the ambient temperature were 20C, hence the electric resistance were 2.74 ohms/km. When current starts passing through the cable, the electric resistance will increase due to increasing temperature, and the power losses in the cable will increase:

P = I² * R.

Including this in the calculations will make a big difference.

I will suggest a program, doing a numerical integration with at least 10800 calculation steps ( 1 per second ).
( You asked for the calculation step by step )

 

[Jeff Rosenbury]

You will also need to know your heat dissipation modes. There are equations for each mode (radiative, conductive, convective). They should be easy to find, but each will involve some estimation. Ideally you should do an error analysis to cover the estimation errors.

Using Hesch's integration:

1. Heat is produced. These are I²R losses, remembering that R is complex for AC transmission lines and depends on geometry and temperature.
   
2. Heat conducts to the surface of the cable. This will depend on the thermal conductance of the material(s). Use a layered approach if your cable has layers.
   
3. Heat that doesn't make it out, heats the material depending on the specific heat of the material(s). The cable likely stretches with heating. This depends on the material, but also on how it is twisted. Heated cable tends to untwist a little making it longer and thinner. I have no idea where to get a formula for this effect. Perhaps someone else knows?
   
4. Heat leaves the cable through the three methods above.

This calculation will need to be done every second or so until thermal equilibrium is reached.

In the end though, you will need to run tests just to be sure.

Or you could read the data supplied by the manufacturer.

As my very rough estimate: A bit under 50º C.

 

[Nidum]

Neher / McGrath method