A two$-$pass tube, baffled single$-$pass shell, shell$-$and$-$tube heat exchanger is used as an oil cooler. Cooling water flows through the tubes at $20\backslash$deg $\backslash$deg C at a flow rate of $4\mathrm{.}082$ kg$/$s$.$ Engine oil enters the shell side at a flow rate of $10$ kg$/$s$.$ The inlet and outlet temperatures of oil are $90\backslash$deg C and $60\backslash$deg C$,$ respectively. Determine the surface area of the heat exchanger by both the LMTD and E$-$NTU methods if the overall heat transfer coefficient based on the outside tube area is $262$ W$/$m$\text{'}.$ K$.$ The specific heats of water and oil are $4179$ J$/$kg$-$K and $2118$ J$/$kg K$,$respectively, Take correction factor $=0\mathrm{.}85$