Question

Three identical metal rods `A`, `B` and `C` are placed end to end and a temperature difference is maintained between the free ends of `A` and `C`. If the thermal conductivity of `B(K_(B))` is twice that of `C(K_(C ))` and half that of `A(K_(A))`, `(K_(A)=49w//mK)` calculate the effective thermal conductivity of the system ?

Answer 1

`K_(B)=K_(A)//2`
`K_(C )=K_(A)//4`
`(1)/(R_(eq))=(L)/(A)((1)/(K_(A))+(1)/(K_(B))+(1)/(K_(C )))=(3L)/(A)((1)/(K_(eff)))`
`K_(eff)=(3K_(A))/(7)=21w//mK`