How to calculate temperature in Wire?

Question

Let's say I have 1m of 2,5mm² copper wire, insulated with H07V-K. The wire carries 40A and environment temperature is 25°C. The wire is suspended in free air. How hot will the wire get? And how can I calculate it for other values?

The use case is a 12V-230V AC converter I want to hook up to my car and determine the minimum wire thickness required. Because it's only used from time to time and not buried in a wall I suspect I can use thinner wires. This is a temporary thing and doesn't need to be up to code.

Answer 1

Is the 40A on the 12V side (480W) or the 230V side (9200W)?

2.5 mm² wire has a resistance of 6.7 mΩ per meter, which means a voltage drop of 0.27 volts per meter. You probably can't tolerate more than about a 10% drop, which is only a total of 1.2 V on the low-voltage side — therefore, you can only use a total of about 4.4 m of wire (two runs of 2.2m).

Anyway, the power dissipation is (40 A)² × 6.7 mΩ = 10 W per meter, which is a lot. The actual temperature rise is difficult to calculate; among other things, we'd need to know the thermal conductivity and thickness of the wire's insulation.

I personally wouldn't use less than AWG8 (roughly 8 mm², 2 mΩ/m) in an application like this, no matter how "temporary" it might be. And don't forget that each connection adds a little resistance, too.

Answer 2

Amount of thermal energy transferred to copper or "Calculate Temperature rise over time in copper due to current flow"

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Must find mass (m) per distance of run of copper wire (in grams) \$\text{Power (W)} = I_{\text{rmsamps}}^2 \times R\text{ }(\Omega)\$

\$\text{Energy (joules)} = P\text{ (W)} \times \Delta T\text{ (seconds)}\$

specific heat of copper (SH) = 0.385 Joules/gram*degree C

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\$\Delta T =\frac{\text{Energy}}{\text{SH}} \times\text{mass}\$

Answer 3

Well, it really depends on many aspects. But for these small wire sizes, the insulation actually improves cooling as the gains in larger surface area initially offset the temperature difference across the insulation walls. There is an interactive app in analyticalviews.com that shows this. Also the amount of connections does not play a role, as the cable is surely long enough (in diameter units) so that its middle section will not be affected by the temperature of the heat sinks (at the end of the cable)