A 2-shell passes and 4-tube passes heat exchanger is used for heating a
hydrocarbon stream \(\left(c_{p}=2.0 \mathrm{~kJ} / \mathrm{kg} \cdot
\mathrm{K}\right)\) steadily from \(20^{\circ} \mathrm{C}\) to \(50^{\circ}
\mathrm{C}\). A water stream enters the shellside at \(80^{\circ} \mathrm{C}\)
and leaves at \(40^{\circ} \mathrm{C}\). There are 160 thin-walled tubes, each
with a diameter of \(2.0 \mathrm{~cm}\) and length of \(1.5 \mathrm{~m}\). The
tube-side and shell-side heat transfer coefficients are \(1.6\) and \(2.5
\mathrm{~kW} / \mathrm{m}^{2} \cdot \mathrm{K}\), respectively. (a) Calculate
the rate of heat transfer and the mass rates of water and hydrocarbon streams.
(b) With usage, the outlet hydrocarbon-stream temperature was found to
decrease by \(5^{\circ} \mathrm{C}\) due to the deposition of solids on the tube
surface. Estimate the magnitude of fouling factor.