GATE Mechanical Engineering (ME) 2019 Shift 1 Solved Paper

Question : 31 of 65

Marks: +1, -0

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

2 {L}

. The heat transfer in radial direction and contact resistance are negligible. The effective thermal conductivity of the composite rod is

Solution:

R_{t h}=\;{∆ T}/{Q}=\;{L}/{k A}

This will be the series connection

R_{t h_{e q}}=R_{t h_{1}}+R_{t h_{2}}

̥or,

\;{2 L}/{k_{e q} A}=\;{L}/{k_{1} A}+\;{L}/{k_{2} A}

\;{2}/{k_{e q}}=\;{1}/{k_{1}}+\;{1}/{k_{2}}

⇒ k_{e q}=\;{2 k_{1} k_{2}}/{k_{1}+k_{2}}

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