# A cylinder of radius r and thermal conductivity $\;K_{1}\;$ is surrounded by cylindrical shell of inner radius r and outer radius 2r and thermal conductivity $\;K_{2}\;$ . The effective thermal conductivity when ends of combined system $\;t_{1}\;$ and $\;t_{2}\;$ under steady state is
$(a)\;(\large\frac{K_{2}+3K_{1}}{4})\qquad(b)\;(\large\frac{3K_{2}+K_{1}}{4})\qquad(c)\;\large\frac{K_{1}}{4}\qquad(d)\;\large\frac{K_{2}}{4}$