Thermal Resistance to Centerline

[terryphi]

Hello,

Given an infinitely long cylinder with a specified surface heat flux,

the thermal resistance of an annular region is given by,

R_th = ln(r_out / r_in) / (2 pi L k).

When I'm calculating the thermal resistance to the centerline, r_in = 0.

Does that mean there is infinite thermal resistance?

 

[mfb]

“Yes”. A finite heat flow to a single line is unphysical.

 

[Chestermiller]

The resistance is infinite and, to have a finite rate of radial heat flow, you would need to have an ideal line heat source at r=0, featuring an infinite temperature gradient at r=0 and an infinite temperature.