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.