A double-pipe parallel-flow heat exchanger is used to heat cold tap water with
hot water. Hot water $\left(c_{p}=4.25 \mathrm{~kJ} / \mathrm{kg} \cdot
\mathrm{K}\right)\( enters the tube at \)85^{\circ} \mathrm{C}$ at a rate of
\(1.4 \mathrm{~kg} / \mathrm{s}\) and leaves at \(50^{\circ} \mathrm{C}\). The
heat exchanger is not well insulated, and it is estimated that 3 percent of
the heat given up by the hot fluid is lost from the heat exchanger. If the
overall heat transfer coefficient and the surface area of the heat exchanger
are \(1150 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\) and $4
\mathrm{~m}^{2}$, respectively, determine the rate of heat transfer to the
cold water and the log mean temperature difference for this heat exchanger.