A heat exchanger with $1$ body and $1$ pipe passage with parallel flow in the Kurchid direction is used to cool the engine oil in a large industrial gas turbine. Wall thickness neglected

Cooling water flowing from the inner pipe $($Di $=25$ mm$)$ at a level that can be achieved is $0\mathrm{.}20$ kg$/$s

At the flow rate, the oil flowing in the space between the outer pipe $($Do $=45$ mm$)$ and the inner pipe is $0\mathrm{.}1$ kg$/$s$.$

is in its flow rate. The entrance temperatures of oil and water to the heat exchanger are $100\backslash$deg C and $30\backslash$deg C$,$ respectively.

How long should the pipe be in order for the oil outlet temperature to be $60\backslash$deg C$?$

It is at its values. Oil

Note: Assume that the expression h$2$ Dh$/$kj$=5\mathrm{.}56$ is valid for the gap between two pipes.

Data: Oil: Cp$=2\mathrm{.}131$ kj$/$kg k p$=3\mathrm{.}25$x$10^-2$ N$.$s$/$m$^2,$ k$=0\mathrm{.}138$ W$/$m$.$K