$2520k\frac{g}{h}$ of oil is to be cooled from $180C$ to $110C$ in a countercurrent heat exchanger as shown in the figure below.

The cooling water, which enters the heat exchanger at $15C,$ is mixed with water at $30C$ at the exit of the heat exchanger to obtain $2415k\frac{g}{h}$ of process water at $60C$ to be used in another location of the plant. Assume that oil and water have constant heat capacities of $2\mathrm{.}3$ and $4\mathrm{.}2k\frac{J}{kg.K},$ respectively.

i$)$ Calculate the mass flow rate of water $(k\frac{g}{h})$ passing through the heat exchanger.

ii$)$ Estimate the total effective heat transfer area in $m^2$ within the heat exchanger if the average overall heat transfer coefficient $(U_0)$ is given as $1000\frac{W}{m^2.K}.$