Inner surface of a cylindrical shell of length $l$ and of material of thermal conductivity $k$ is kept at constant temperature $T_{1}$ and outer surface of the cylinder is kept at constant temperature $T_{2}$ such that $T_{1}>T_{2}$ as shown in Fig. 11.3. Heat flows from inner surface to outer surface radially outward. Inner and outer radii of the shell are $R$ and $2 R$, respectively. Due to lack of space, this cylinder has to be replaced by a smaller cylinder of length $\frac{l}{2}$, inner and outer radii $\frac{R}{4}$ and $R$, respectively, and thermal conductivity of material $n k$. If rate of radial outward heat flow remains same for same temperatures of inner and outer surface, i.e., $T_{1}$ and $T_{2}$, then find the value of $n$.