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 \(20^{\circ} \mathrm{C}\) at a flow rate of \(4.082 \mathrm{~kg} / \mathrm{s}\). Engine oil enters the shell side at a flow rate of \(10 \mathrm{~kg} / \mathrm{s}\). The inlet and outlet temperatures of oil are \(90^{\circ} \mathrm{C}\) and \(60^{\circ} \mathrm{C}\), respectively. Determine the surface area of the heat exchanger by the e-NTU method if the overall heat transfer coefficient based on the outside tube area is \(262 \mathrm{~W} / \mathrm{m}^{2}-\mathrm{K}\). The specific heats of water and oil are \(4179 \mathrm{~J} / \mathrm{kg}-\mathrm{K}\) and \(2118 \mathrm{~J} / \mathrm{kg}-\mathrm{K}\), respectively.