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 figure. Heat flows from inner surface to outer surface radially outward. Inner and outer radii of the shell are R and 2R respectively. Due to lack of space this cylinder has to be replaced by a smaller cylinder of length  $\frac{\mathcal{l}}{2}$, inner and outer radii $\frac{R}{4}$ and R respectively and thermal conductivity of material nk. If rate of radial outward heat flow remains same for same temperature of inner and outer surface i.e, $T_1$ and  $T_2$, then find the value of n