Heat Exchangers Questions and Answers

Answer: A

The key says that oil coolers are an application of straight tube, fixed tubesheet heat exchangers. In this type the tubes are welded to tubesheets fixed in the shell, so the outside of the tubes cannot be cleaned mechanically, and the type is used where the shell side fluid is clean, as with oil. A fluid that is flammable or toxic in the tubes, or a cooler with water inside the tubes, is not the keyed application, and jacket water coolers are not the keyed application either.

Answer: D

The advantage of a removable bundle U-tube type heat exchanger is that the shell circuit can be inspected and mechanically cleaned, since the whole bundle can be pulled out. A single tube pass is not possible in a U-tube exchanger, because the fluid has to go down one limb and back up the other. The tube wall thickness at the U-bend is thinner and not thicker, and the tubes in the nest cannot be easily replaced individually, so the other statements are not advantages.

Answer: C

The correction factor applies to a plate heat exchanger.

The LMTD formula is exact only for pure counter-flow or parallel-flow arrangements. For multi-pass and cross-flow arrangements, such as most plate heat exchangers with their several passes and channel patterns, the true mean temperature difference is the counter-flow LMTD multiplied by a correction factor \(F \le 1\).

In a steam-jacketed kettle and in evaporator tubes, one side is condensing steam at constant temperature, so the flow arrangement does not matter and \(F = 1\). A single spiral tube is effectively a simple counter- or co-current exchanger and is not where the correction factor is characteristically used.

Answer: B

No correction factor is needed for a 1 shell pass and 1 tube pass heat exchanger.

The LMTD formula is exact only for pure parallel flow or pure counterflow. A 1-1 shell-and-tube exchanger is one of these: the shell fluid and tube fluid each make a single pass, so the exchanger is analysed directly as counterflow (or parallel flow) with F = 1.

In 1-2 and 2-4 shell-and-tube exchangers the tube fluid reverses direction, so part of the exchanger runs in parallel flow and part in counterflow; the true mean temperature difference is less than the counterflow LMTD and a correction factor F below 1 is applied. Plate heat exchangers are also normally treated with a correction factor, because their pass and channel arrangements depart from pure counterflow; the key takes the 1-1 shell-and-tube exchanger as the case that needs none.

Answer: A

The dimensionless one is heat exchanger effectiveness.

Effectiveness is the actual heat transfer rate divided by the maximum possible rate for the same inlet conditions, \(\varepsilon = q/q_{max}\). Both are in watts, so the ratio has no unit and lies between 0 and 1.

The others all carry units. Humid heat is the heat needed to warm 1 kg of dry air and its vapour by 1 K, in kJ.kg⁻¹.K⁻¹. Humid volume is the volume of moist air per kg of dry air, in m³.kg⁻¹. The overall heat transfer coefficient is in W.m⁻².K⁻¹.

Answer: C

The LMTD is 10 °C.

The heat capacity rates are equal:

\[ \begin{aligned} C_{w} &= 0.5 \times 4.18 = 2.09\ \text{kW/K} \\ C_{a} &= 2.09 \times 1 = 2.09\ \text{kW/K} \end{aligned} \]

With effectiveness 0.8 and a maximum temperature difference of 80 - 30 = 50 °C, each stream changes by 0.8 × 50 = 40 °C: water leaves at 40 °C and air at 70 °C. In a counterflow exchanger with equal capacity rates, the temperature difference is the same at both ends, 80 - 70 = 40 - 30 = 10 °C, so the LMTD equals that constant difference.

40 °C is the temperature change of each stream, 20 °C and 5 °C have no basis here. A check: Q = 2.09 × 40 = 83.6 kW, and UA = Q/LMTD = 8.36 kW/K, so NTU = 4 and \(\varepsilon = 4/5 = 0.8\).