A thermometer pocket, $2\mathrm{.}2$cm is diameter $0\mathrm{.}5$mm thick is made of steel $($k$=27$W$/$m$^2$K$)$ and itvis used to measure the temperature stream flowing through pipe. Calculate the minimum length of pocket so that the error is less than $0\mathrm{.}5\%$ of the applied temperature difference. Take steam at $250$C and h$=98$W$/$m$^2$K$.$