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I have a confusion about how to calculate the thermal resistance of a solid rod ( not hollow).

The general formula is $$R=\ln(r2/r1)/(2\pi Lk)$$ In my case, $r1=0$

Any hint would be highly appreciated.

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  • $\begingroup$ yes correct, normally in my case, exercices are solved by using temperature distribution equation, but I just wanted to see how to calculate thermal resistance in my case, I thought that maybe I could put r1=0.01 but still someone has a better idea? $\endgroup$
    – Ama Ouchen
    Commented Jan 7, 2019 at 9:18
  • $\begingroup$ I need to confirm that there is no direct formula , maybe the only solution is to Q˙=ΔT/R so we need to find heat transfer rate and the ΔT before calculating?? $\endgroup$
    – Ama Ouchen
    Commented Jan 7, 2019 at 9:24
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    $\begingroup$ Use the analogy of ohm's law and heat current $\endgroup$ Commented Jan 7, 2019 at 10:00
  • $\begingroup$ yes, I guess this is what I mentioned, thanks for confirming! $\endgroup$
    – Ama Ouchen
    Commented Jan 7, 2019 at 10:01
  • $\begingroup$ Sorry, on reflection I have realised that the formula that you have quoted predicts the heat flow through the walls of a pipe not along the length of a pipe. $\endgroup$
    – Farcher
    Commented Jan 7, 2019 at 10:06

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As the inner radius tends to towards zero the inner area through which the heat has to flow also tends to zero and this is the reason for the thermal resistance tending to infinity.

So you have the correct formula which correctly predicts that, as the inner radius tend to zero, the thermal resistance tends to infinity.

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  • $\begingroup$ so according to you, R is very large and by consequence, the heat transfer is almost null? q=ΔV/R $\endgroup$
    – Ama Ouchen
    Commented Jan 7, 2019 at 10:15
  • $\begingroup$ The formula is for a tube containing a source of heat which is lost through the walls. If the inner radius is exactly zero, obviously there is no source of heat and so no loss. Before applying maths it is worthwhile to look at the physics. $\endgroup$ Commented Jan 8, 2019 at 4:15

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