Consider a cylindrical shell with an inner diameter of $0\mathrm{.}1$ m and outer diameter of $0\mathrm{.}2$ m whose thermal conductivity varies linearly in a

specified temperature range as k$($r$)=$ k$0/$ln$($r$/$r$0)$ where k$0=12$ W$/$m K and r$0$ is the inner radio. The inner surface of the shell is maintained at a

constant temperature of $250$C$,$ while the outer surface is maintained at $25$C$.$ Find the heat transfer per unit length.

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