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COMEDK · Physics · 12. Thermal Properties of Matter

A cylinder of radius \(r\) and of thermal conductivity \(K_1\) is surrounded by a cylindrical shell of inner radius \(r\) and outer radius \(2 r\) made of a material of thermal conductivity \(K_2\). The effective thermal conductivity of the system is

  1. A \(\dfrac{1}{4}\left(K_1+3 K_2\right)\)
  2. B \(\dfrac{1}{3}\left(3 K_2+2 K_1\right)\)
  3. C \(\dfrac{1}{2}\left(2 K_1+3 K_2\right)\)
  4. D \(\dfrac{1}{3}\left(K_1+2 K_2\right)\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\dfrac{1}{4}\left(K_1+3 K_2\right)\)

Step-by-step Solution

Detailed explanation

Consider a length \(L\) of the composite cylinder. The system consists of two cylindrical layers in parallel for radial heat flow. The thermal resistance \(R\) of a cylindrical shell of inner radius \(r_1\), outer radius \(r_2\), length \(L\), and thermal conductivity \(K\) is…