Inner surfaec 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)gtT_(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 resspectively. Due to lack of space this cylinder has to be replaced by a smaller cylinder of length `(l)/(2)` inner and outer radii `(R)/(4)` and R respectively and thermal conductivity of material nk. if rate of radially 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.

Explanation

`H=-K.2pirl(dT)/(dr)`
`int_(R_(1))^(R_(2))(Hdr)/(2pirl)=-Kint_(T_(1))^(T_(2))dT`
`H=(2pilk(T_(1)-T_(2)))/(ln((R_(2))/(R_(1))))`
`H_(i)=H_(f)`
`thereforen=4`