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GATE2019 ME-1: 11

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A slender rod of length $L$, diameter $d$ $(L > >d)$ and thermal conductivity $k_1$ is joined with another rod of identical dimensions, but of thermal conductivity $k_2$, to form a composite cylindrical rod of length $2L$. The heat transfer in radial direction and contact resistance are negligible. The effective thermal conductivity of the composite rod is

  1. $k_1+k_2 \\$
  2. $\sqrt{k_1k_2} \\$
  3. $\dfrac{k_1k_2}{k_1+k_2} \\$
  4. $\dfrac{2k_1k_2}{k_1+k_2}$
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