I'm reading about how to calculate the power transferred though conduction, but I'm unclear about how to apply it to a problem. The formula that I have for this is:

$\frac{Q}{t}=k \frac{A}{l} (T_h-T_c)$

Where Q is energy, t is time, k is thermal conductivity, A is area, l is length, Th is the temperature of the hotter medium and Tc is the temperature of the colder medium.

If you have a wire with a given cross sectional area, length and thermal conductivity constant, how would you calculate the power lost to the colder environment?

I can imagine that if you wanted to know the heat transfer from one end of the wire to the other you'd use the length of the wire as the length in the equation and the cross sectional area of the wire as the area in the equation. Would the area be the surface area of the wire and the length be the radius of the wire if you wanted to calculate the heat flow from the wire to the air?

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    $\begingroup$ If you wanted to consider the rate of heat loss to the air, you would have to focus on the so-called convective heat transfer in the air surrounding the wire. This is where the main resistance to heat transfer would reside. This convective heat transfer is usually quantified in terms of a convective heat transfer coefficient h, which is related to the heat flow by $Q=2πRLh(T_{wire}−T_{air})$ $\endgroup$ – Chet Miller Jun 3 '17 at 14:53

Your formula is specific to uniform cylindrical structures and heat transfer by conduction.

Transfer from the surface of the wire to the air involves non-cylindrical geometry, nonuniform material, and convective transfer, so you'd need an entirely different formula or possibly numerical analysis to determine the heat transfer.


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