A heat exchanger is operated at a flow rate of \(30 \mathrm{~kg} / \mathrm{s}\) and water enters at \(20{ }^{\circ} \mathrm{C}\) and leaves at \(80^{\circ} \mathrm{C}\). Find the length of exchanger needed if the (average) heat transfer coefficient is \(200 \mathrm{~W} / \mathrm{K} \cdot \mathrm{m}^{2}\).

Solve the above problem if a constant inward wall flux of \(2 \mathrm{~W} / \mathrm{m}^{2}\) is introduced instead of a constant wall temperature.