$11.$ A countercurrent flow double pipe heat exchanger is used to heat water flowing at $1$ kg$/$s from $40\backslash$deg C to $80\backslash$deg C$.$ Oil is used for heating and its temperature changes from $100\backslash$deg C to $70\backslash$deg C$.$ The overall heat transfer coefficient is $300$ W$/($m$^2\backslash$deg C$).$ If it is replaced by a $1-2$ shell and tube heat exchanger with countercurrent flow configuration with water flowing in shell and oil flowing in the tube, what is the excess area required with respect to the double pipe heat exchanger?

The correction factor, F$$ for LMTD $($Log Mean Temperature Difference$)$ based on the above double pipe heat exchanger is $0\mathrm{.}5.$ The heat transfer coefficient remains unchanged, and the same inlet and outlet conditions are maintained.

Cp$.$ water $=4180$ J$/$kg$\backslash$deg C$,$ CD$.$ oil $=2000$ J$/$kg $\backslash$deg C$,$