Chapter 11

An air handler is a large unmixed heat exchanger used for comfort control in large buildings. In one such application, chilled water $\left(c_{p}=4.2 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K}\right)$ enters an air handler at \(5^{\circ} \mathrm{C}\) and leaves at \(12^{\circ} \mathrm{C}\) with a flow rate of \(1000 \mathrm{~kg} / \mathrm{h}\). This cold water cools $5000 \mathrm{~kg} / \mathrm{h}\( of air \)\left(c_{p}=1.0 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K}\right)\( which enters the air handler at \)25^{\circ} \mathrm{C}$. If these streams are in counterflow and the water-stream conditions remain fixed, the minimum temperature at the air outlet is (a) \(5^{\circ} \mathrm{C}\) (b) \(12^{\circ} \mathrm{C}\) (c) \(19^{\circ} \mathrm{C}\) (d) \(22^{\circ} \mathrm{C}\) (e) \(25^{\circ} \mathrm{C}\)

An air handler is a large unmixed heat exchanger used for comfort control in large buildings. In one such application, chilled water $\left(c_{p}=4.2 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K}\right)$ enters an air handler at \(5^{\circ} \mathrm{C}\) and leaves at \(12^{\circ} \mathrm{C}\) with a flow rate of \(1000 \mathrm{~kg} / \mathrm{h}\). This cold water cools air \(\left(c_{p}=1.0 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K}\right)\) from \(25^{\circ} \mathrm{C}\) to \(15^{\circ} \mathrm{C}\). The rate of heat transfer between the two streams is (a) \(8.2 \mathrm{~kW}\) (b) \(23.7 \mathrm{~kW}\) (c) \(33.8 \mathrm{~kW}\) (d) \(44.8 \mathrm{~kW}\) (e) \(52.8 \mathrm{~kW}\)

In a parallel-flow, liquid-to-liquid heat exchanger, the inlet and outlet temperatures of the hot fluid are \(150^{\circ} \mathrm{C}\) and $90^{\circ} \mathrm{C}\( while those of the cold fluid are \)30^{\circ} \mathrm{C}$ and \(70^{\circ} \mathrm{C}\), respectively. For the same overall heat transfer coefficient, the percentage decrease in the surface area of the heat exchanger if counterflow arrangement is used is (a) \(3.9 \%\) (b) \(9.7 \%\) (c) \(14.5 \%\) (d) \(19.7 \%\) (e) \(24.6 \%\)

A counterflow heat exchanger is used to cool oil $\left(c_{p}=2.20 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K}\right)\( from \)110^{\circ} \mathrm{C}\( to \)85^{\circ} \mathrm{C}\( at a rate of \)0.75\( \)\mathrm{kg} / \mathrm{s}\( with cold water \)\left(c_{p}=4.18 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K}\right)\( that enters the heat exchanger at \)20^{\circ} \mathrm{C}$ at a rate of \(0.6 \mathrm{~kg} / \mathrm{s}\). If the overall heat transfer coefficient is \(800 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\), the heat transfer area of the heat exchanger is (a) \(0.745 \mathrm{~m}^{2}\) (b) \(0.760 \mathrm{~m}^{2}\) (c) \(0.775 \mathrm{~m}^{2}\) (d) \(0.790 \mathrm{~m}^{2}\) (e) \(0.805 \mathrm{~m}^{2}\)

The radiator in an automobile is a crossflow heat exchanger $\left(U A_{s}=10 \mathrm{~kW} / \mathrm{K}\right)\( that uses air \)\left(c_{p}=1.00 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K}\right)$ to cool the engine coolant fluid \(\left(c_{p}=4.00 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K}\right)\). The engine fan draws \(30^{\circ} \mathrm{C}\) air through this radiator at a rate of \(12 \mathrm{~kg} / \mathrm{s}\) while the coolant pump circulates the engine coolant at a rate of \(5 \mathrm{~kg} / \mathrm{s}\). The coolant enters this radiator at \(80^{\circ} \mathrm{C}\). Under these conditions, what is the number of transfer units (NTU) of this radiator? (a) \(2.0\) (b) \(2.5\) (c) \(3.0\) (d) \(3.5\) (e) \(4.0\)

In a parallel-flow, water-to-water heat exchanger, the hot water enters at \(75^{\circ} \mathrm{C}\) at a rate of \(1.2 \mathrm{~kg} / \mathrm{s}\) and cold water enters at \(20^{\circ} \mathrm{C}\) at a rate of $0.9 \mathrm{~kg} / \mathrm{s}$. The overall heat transfer coefficient and the surface area for this heat exchanger are \(750 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\) and \(6.4 \mathrm{~m}^{2}\), respectively. The specific heat for both the hot and cold fluids may be taken to be $4.18 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K}$. For the same overall heat transfer coefficient and the surface area, the increase in the effectiveness of this heat exchanger if counterflow arrangement is used is (a) \(0.09\) (b) \(0.11\) (c) \(0.14\) (d) \(0.17\) (e) \(0.19\)

In a parallel-flow heat exchanger, the NTU is calculated to be \(2.5\). The lowest possible effectiveness for this heat exchanger is (a) \(10 \%\) (b) \(27 \%\) (c) \(41 \%\) (d) \(50 \%\) (e) \(92 \%\)

Cold water $\left(c_{p}=4.18 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K}\right)\( enters a counterflow heat exchanger at \)10^{\circ} \mathrm{C}\( at a rate of \)0.35 \mathrm{~kg} / \mathrm{s}$, where it is heated by hot air $\left(c_{p}=1.0 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K}\right)\( that enters the heat exchanger at \)50^{\circ} \mathrm{C}$ at a rate of \(1.9 \mathrm{~kg} / \mathrm{s}\) and leaves at $25^{\circ} \mathrm{C}$. The effectiveness of this heat exchanger is (a) \(0.50\) (b) \(0.63\) (c) \(0.72\) (d) \(0.81\) (e) \(0.89\)

Steam is to be condensed on the shell side of a twoshell-passes and eight- tube-passes condenser, with 20 tubes in each pass. Cooling water enters the tubes at a rate of \(2 \mathrm{~kg} / \mathrm{s}\). If the heat transfer area is \(14 \mathrm{~m}^{2}\) and the overall heat transfer coefficient is $1800 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}$, the effectiveness of this condenser is (a) \(0.70\) (b) \(0.80\) (c) \(0.90\) (d) \(0.95\) (e) \(1.0\)

Water is boiled at \(150^{\circ} \mathrm{C}\) in a boiler by hot exhaust gases $\left(c_{p}=1.05 \mathrm{~kJ} / \mathrm{kg}^{\circ}{ }^{\circ} \mathrm{C}\right)\( that enter the boiler at \)540^{\circ} \mathrm{C}$ at a rate of \(0.4 \mathrm{~kg} / \mathrm{s}\) and leave at \(200^{\circ} \mathrm{C}\). The surface area of the heat exchanger is \(0.64 \mathrm{~m}^{2}\). The overall heat transfer coefficient of this heat exchanger is\(\mathrm{kg} / \mathrm{s}\) with cold water $\left(c_{p}=4.18 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K}\right)\( that enters the heat exchanger at \)20^{\circ} \mathrm{C}$ at a rate of \(0.6 \mathrm{~kg} / \mathrm{s}\). If the overall heat transfer coefficient is \(800 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\), the heat transfer area of the heat exchanger is (a) \(0.745 \mathrm{~m}^{2}\) (b) \(0.760 \mathrm{~m}^{2}\) (c) \(0.775 \mathrm{~m}^{2}\) (d) \(0.790 \mathrm{~m}^{2}\) (e) \(0.805 \mathrm{~m}^{2}\)