Question

Thermal conductivity of inner core of radius r is K and of the outer one of radius `2r` is 2K. Find equivalent value of thermal conductivity between its two ends.

Answer 1

Here `A_1=piR^2`,`K_1=K`
And `A_2=4piR^2-piR^2=3piR^2`,`K_2=2K`
Using, the expression for the effective thermal conductivity for slabs in parallel,
`K_(eff)=(A_1K_1+A_2K_2)/(A_1+A_2)`
`=(piR^2(K)+3piR^2(2K))/(piR^2+3piR^2)=(7K)/(4)`