A cylinder of radius r and of thermal conductivity k1 is surrounded by a cylindrical shell of inner radius r and outer radius 2r made of a material of thermal conductivity k2. The effective thermal conductivity of the system is
Since the two cylinders are in parallel, the equivalent thermal resistance R of the combination is given by
1R=1R1+1R2
or kAl=k1A1l1+k2A2l2 (1)
Now A=π(2r)2=4πr2, A1=πr2,A2=π[(2r)2−r2]=3πr2 and l1=l2=l. Using these in (1), we get
4k=k1+3k2or k=14(k1+3k2)
Hence the correct choice is (d).