I am trying to calculate how hot will a 0.6m long 28AWG wire carrying a load of 12VDC, 0.2A get.
I understand that are other factors such as environment cooling rate, thermal resistance between air and the cable etc.
Ampacity values are not really relevant to my scenario as the cable is in contact with the human body. Thus, I am more concerned about whether if the user can detect the change in the wire's temperature.
I also do not have the resources nor the proper apparatus to conduct an accurate measurement test.
An aluminium core 28AWG wire has a resistance of 0.32716 Ω/m.
Power dissipation:
$$P=I^2R$$
$$P=0.2A^2\times0.32716Ω \times 0.6m$$
$$P=7.851mW$$
Found this equation here, altough it is only meant for radiative heat loss
$$ \dot{Q}_{12} = \epsilon A\left ( \sigma T_1^4 – \sigma T_2^4\right )$$
Based on the above, I got a value of \$309K\$ which means the temperature increase is about \$4°C\$ from an ambient temp of \$305K\$.
Is this an accurate reference?
Basically, I want to know if a 28AWG wire will stay cool during operation or do I need to select a lower gauge wire.
Best Answer
Radiation is a negligible component of heat loss for a wire close to room temperature in air. It becomes a factor for long wires in a vacuum, and high temperature differences, but that's not the case here. Convection is the primary source of heat loss for a long wire in still (or moving) air.
If it's in contact with skin, conduction will be a big factor. In air, convection is the primary factor. Convection calculations involve fluid dynamics so they're not as straightforward as you might hope for. But to get a rough estimate, consider this graph from this website:
Very roughly the temperature rise in still air is about 3.3\$\times \text I^2\$, so for a current of 200mA in an AWG 28 wire you could expect about a 0.15K rise. If it's in contact with a 'bag of mostly water' the conduction to the skin (and therefore the skin temperature) will have a large effect.