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Consider a coaxial cable that has a copper core conductor and polyethylene dielectric with the following properties: Core conductor resistivity of 19 nohm m, core radius of 4 mm, dielectric thickness of 3.5 mm, dielectric thermal conductivity of 0.3 W (mK)^{1}. The outside temperature is 25^{o}C. The cable is carrying a current of 500A. What is the temperature of the inner conductor? 

Solution
We need to apply the Fourier's law of heat conduction. Consider a small element of thickness dr at a distance r from the center of the coaxial cable of length L as shown in the figure below. The surface area of this element will be . Now apply the Fourier's law:
Or,
Or,
Or,
Solving this integration gives a general equation for a coaxial cable:
Where, thermal resistance
The outside temperature, T_{o}, is 25 + 273 = 298 K. We have been asked to determine the inside temperature, T_{i}, for which we can use the general equation derived above. Now we need to determine the heat flow per unit time (Q^{'}).
= 94.498L Watts
and from the thermal resistance formula we get KW^{1}.
Now using the equation , we find =  31.468 K.
Therefore, the inner temperature (T_{i}) = 31.468 + 298 = 329.468 K or 56.468^{o}C.