A cylinder of radius R is surrounded by a cylindrical shell of inner radius R and oputer radius 2R. The thermal conductivity of the material of the inner cylinder is `k_(1)` and that of the outer cylinder is `K_(2)` ,Assumming no loss of heat , the effective thermal conductivity of the system for heat flowing along the length of the cylinder is :

Options

A. `(2K_(1)+3K_(2))/(5)`
B. `(K_(1)+3K_(2))/(4)`
C. `K_(1)+K_(2)`
D. `(K_(1)+K_(2))/(2)`

Answer

B

Explanation

`R=(L)/(KA),R_(1)=(l)/(K_(1)piR^(2)),R_(2)=(l)/(K_(2)pi(4R^(2)-l^(2)))`
`(1)/("Req")=(1)/(R//1)+(1)/(R_(2))`
`("Keq"xx4piR^(2))/(l)=(K_(1)piR^(2))/(l)+(3K_(2)piR^(2))/(l),"Keq"=(K_(1)+3K_(2))/(4)`