It is desired to cool $1\mathrm{.}2kg*s^{-1}$ engine oil from $90oC$ to $50C$ using cooling water available at $10C$ and flow of $1\mathrm{.}0kg.s^{-1}.$ Design a suitable shell$-$and$-$tube heat exchanger $($with no baffles$),$ which is made of steel $)=(16W{m}^{-10}{C}^{-1}$ to perform this heat duty. The only condition set by your client is that the length of the heat exchanger should not exceed $5m$