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Equivalent thermal conductivity

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Problem

A small cylinder of radius r is placed inside a big shell having inner radius r and external radius 4r. The ends of the cylinders are maintained at different temperatures as represented below.
The conductivity of the inner cylinder is 5K and that of the outer cylindrical shell is 2K.
Find the equivalent thermal conductivity of the system in terms of K.
Note: Report your answer as a fraction.
keff.=
  • Your answer should be
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
K