GATE ME 2019 Set 1 — Question 21
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Heat Transfer → Conduction → Composite Wall Conduction
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Question
A slender rod of length , diameter () and thermal conductivity is joined with another rod of identical dimensions, but of thermal conductivity , to form a composite cylindrical rod of length . The heat transfer in radial direction and contact resistance are negligible. The effective thermal conductivity of the composite rod is
Correct answer
(D) (2 k₁ k₂)/(k₁ + k₂)
Solution
The two rods are connected in series. The total thermal resistance is the sum of the individual thermal resistances and .
For a cylindrical rod, thermal resistance is given by , where is length, is thermal conductivity, and is cross-sectional area.
Dividing by :
For a cylindrical rod, thermal resistance is given by , where is length, is thermal conductivity, and is cross-sectional area.
Dividing by :
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