Three slabs of same surface area but different conductivities `k_(1),k_(2),k_(3)` and different thickness `t_(1),t_(2),t_(3)` are placed in close contact. After steady state this combination behaves as a single slab. Find its effective thermal conductivity.

Answer

`(t_(1)+t_(2)+t_(3))/((t_(1))/(k_(1))+(t_(2))/(k_(2))+(t_(3))/(k_(3)))`

Explanation

`R_(eq) = R_(1)+R_(2)+R_(3)` (series combination)
`(t_(1)+t_(2)+t_(3))/(K_(eq)A) = (t_(1))/(K_(1)A) +(t_(2))/(K_(2)A) +(t_(3))/(K_(3)A)`
`(t_(1)+t_(2)+t_(3))/(K_(eq)) =(t_(1))/(K_(1)) +(t_(2))/(K_(2)) +(t_(3))/(K_(3))`
`K_(eq) = (t_(1)+t_(2)+t_(3))/((t_(1))/(K_(1))+(t_(2))/(K_(2))+(t_(3))/(K_(3)))`