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Mechanical Engineering QUESTION #2425
Question 1
For steady 1D conduction through a cylindrical wall (inner radius \(r_1\), outer radius \(r_2\), length \(L\), conductivity \(k\)), the thermal resistance is:
  • \(R_{cyl} = \frac{r_2 - r_1}{2\pi r L k}\)
  • \(R_{cyl} = \frac{\ln(r_2/r_1)}{2\pi L k}\)✔️
  • \(R_{cyl} = \frac{2\pi L k}{\ln(r_2/r_1)}\)
  • \(R_{cyl} = \frac{r_2^2 - r_1^2}{2kL}\)
Correct Answer Explanation
For a hollow cylinder: \(R_{cyl}=\ln(r_2/r_1)/(2\pi Lk)\). Temperature varies logarithmically, not linearly as in the plane wall.