Heat transfer in a cylindrical tube

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SUMMARY

The discussion centers on the calculation of heat resistance through a cylindrical tube, specifically using the formula R(heat resistor) = 1/(2πLλ) * ln(R1/R2). A participant expresses confusion regarding the negative values obtained when R1 is smaller than R2, indicating a misunderstanding of the formula. Another contributor clarifies that the correct formula for heat loss in a pipe is Q = 2πkL(T1-T2)/ln(r2/r1), where r1 is the inner radius and r2 is the outer radius, thus resolving the initial confusion.

PREREQUISITES
  • Understanding of heat transfer principles
  • Familiarity with cylindrical coordinates
  • Knowledge of logarithmic functions
  • Basic concepts of thermal conductivity
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  • Study the derivation of the heat transfer equation for cylindrical geometries
  • Learn about thermal conductivity and its impact on heat transfer
  • Explore the application of the natural logarithm in engineering calculations
  • Investigate practical examples of heat loss in pipes and insulation techniques
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Students in engineering or physics, particularly those studying thermodynamics and heat transfer, as well as professionals involved in thermal management and insulation design.

5carola5
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Homework Statement



I don't really understand something in my textbook. It says the heat Resistor (how to say that in English? I hope it's alright like this...) trough a cylindrical tube (from the inside to the outside or revers) would be: R(heatrisistor)=1/2∏Lλ * ln (R1/R2) And then my textbook gives the following picture (well oke a but nicer, but that's what I make of it)http://schattielover.deviantart.com/art/homework-314836756

But if I were to follow this I get a negative R every time (since R1 is smaller than R2 and so the ln gets negative right?), which I find very strange... So I searched trough other textbooks that I have and they had no information about it and searched trough the internet (I'm not very good at that ^^') and found nothing I can use.

So my question is: Can someone explain to me, nice and simple, what I should do with the R1 and the R2? (I probably am misunderstanding my textbook... I'm sure of it ^^')

Well thanks for reading all of this anyway, hope someone can help me with this. :)
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I can't see your diagram but I think there is a mistake. R1 and R2 should be the other way around. See...

http://wiki.answers.com/Q/Formula_for_Heat_loss_in_a_pipe

Q= 2 pi k L(T1-T2)/ln(r2/r1)

where

k=conductivity of material of which pipe is made

T1= temperature of inside layer pipe
T2=temperature outside layer of pipe
L= length of pipe
r1= inner radius
r2=outer radius
ln=natural logrithem
 
thank you so much! I can defiantly do something with that =D =D =D. I can be so stupid sometimes ^^'
 

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