Heat Transfer - Heat Flux (thermal Resistance)

[Icetray]

Homework Statement

Hi guys,

I don't really need help with answering the dollowing question but just have a quick question about it.

I solved the first part of the question with an energy balance by letting q_{conduction} = q_{convection} to get the temperature of he outer surface temperature of the wire.

For the heat flux part, why can't the heat flux = q_{conduction} = q_{convection}? Shouldn't the heat flux be constant throughout?

Thanks in advance guys!

 

[Chestermiller]

Homework Statement

Hi guys,

I don't really need help with answering the dollowing question but just have a quick question about it.

I solved the first part of the question with an energy balance by letting q_{conduction} = q_{convection} to get the temperature of he outer surface temperature of the wire.

For the heat flux part, why can't the heat flux = q_{conduction} = q_{convection}? Shouldn't the heat flux be constant throughout?

Thanks in advance guys!

Because the heat flux is varying with radial position within the wire, and, even if it weren't, the circumferential perimeter available for heat flow is varying with radius. At any radial location, the product of the heat flux and 2πr represents the local radial heat flow per unit length of wire.