A cylinder of radius R made of material of thermal conductivity `K_(1)` is surrounded by a cylindrical shell of inner radius R and outer radius 3R made of a material of thermal conductivity `K_(2)`. The two ends of the combined system are maintained at two different temperatures. What is the effective thermal conductivity of the system ?

Options

A. `K_(1)+K_(2)`
B. `(K_(1)+8K_(2))/(9)`
C. `(K_(1)K_(2))/(K_(1)+K_(2))`
D. `(8K_(1)+K_(2))/(9)`

Answer

B

Explanation

As we use `k_(eq)=(K_(1)A_(t)+K_(2)A_(2))/(A_(1)+A_(2))`
`implies K_(eq)=(K_(1)[piR^(2)]+K_(2)[pi(9R^(2))-piR^(2))]/(piR^(2)+pi(9R^(2)-R^(2)))`
`implies K_(eq)=(K_(1)+8K_(2))/(9)`