A cylinder of radius `R` made of a material of thermal conductivity `K_(1)` is surrounded by cylindrical shell of inner radius `R` and outer radius `2R` made of a material of thermal con-ductivity `K_(2)` The two ends of the combined system are maintained at two differnet tem-peratures There is no loss of heat across the cylindrical surface and system is in steady state What is the effective thermal conductivity of the system
.

Options

A. `k_(1)+k_(2)`
B. `(k_(1)k_(2))/(k_(1)+k_(2))`
C. `(1)/(4)(k_(1)+3k_(2))`
D. `(1)/(4)(3k+k_(2))`

Explanation

`R_(eq)=(R_(1)R_(2))/(R_(1)+R_(2))`
`R_(1)=(l)/(k_(1)(piR^(2)))`, `R_(2)=(l)/(k_(2)3piR^(2))`
`R_(eq)=((l)/(piR^(2)))((l)/(piR^(2)))((l)/(k_(1)k_(2)))((1)/(3))`
`(l)/(piR^(2))(1)/(k_(1))+(1)/(3k_(2))`

`R_(New)=(l)/(k(4piR^(2))=R_(eq)`
`R_(eq)=(l)/(piR^(2))((1)/(3k_(2)+k_(1)))`
`(l)/(piR^(2)(4k))=(l)/(piR^(2))((l)/(3k_(2)+k_(1)))`
`impliesk=(3k_(2)+k_(1))/(4)`