Consider a water-to-water double-pipe heat exchanger whose flow arrangement is not known. The temperature measurements indicate that the cold water enters at \(20^{\circ} \mathrm{C}\) and leaves at \(50^{\circ} \mathrm{C}\), while the hot water enters at \(80^{\circ} \mathrm{C}\) and leaves at \(45^{\circ} \mathrm{C}\). Do you think this is a parallel-flow or counterflow heat exchanger? Explain.

Short Answer

Expert verified
Answer: Based on the temperature measurements provided, the double-pipe heat exchanger is a counterflow arrangement.

Step by step solution

01

Definitions and Distinctions

In a double-pipe heat exchanger, hot and cold fluids flow inside and between two separate pipes, exchanging heat as they move. In a parallel-flow arrangement, both fluids flow in the same direction. On the other hand, in a counterflow arrangement, the fluids flow in opposite directions. The behavior of temperature difference between the hot and cold streams enables us to determine the type of the heat exchanger.
02

Examine the Temperature Measurements

We have the following temperature measurements: - Cold water: enters at 20°C and leaves at 50°C - Hot water: enters at 80°C and leaves at 45°C Let's first determine the temperature difference between the hot and cold water streams at the inlet and outlet points.
03

Calculate the Temperature Difference at Inlet and Outlet

At the inlet, the temperature difference (∆T_in) is the difference between the hot water's entering temperature and the cold water's entering temperature: ∆T_in = T_hot_in - T_cold_in At the outlet, the temperature difference (∆T_out) is the difference between the hot water's leaving temperature and the cold water's leaving temperature: ∆T_out = T_hot_out - T_cold_out Using the given temperatures, we calculate ∆T_in and ∆T_out.
04

Temperature Difference at Inlet

The temperature difference at the inlet is: ∆T_in = 80°C - 20°C = 60°C
05

Temperature Difference at Outlet

The temperature difference at the outlet is: ∆T_out = 45°C - 50°C = -5°C
06

Determine the Heat Exchanger Type

Based on the calculated temperature differences, we observe: 1. At the inlet, the hot water stream is warmer than the cold water by 60°C. 2. At the outlet, the cold water stream is warmer than the hot water by 5°C. This pattern of temperature difference indicates that the hot and cold water streams are flowing in opposite directions, making it a counterflow heat exchanger. In a parallel-flow arrangement, you would expect the hot stream to be warmer than the cold stream for the entire length of the exchanger, which is not the case here. Since the hot water is leaving at a lower temperature than the cold water, it is evident that the hot and cold water streams are moving counter to each other. In conclusion, based on the temperature measurements provided, it can be determined that this double-pipe heat exchanger is a counterflow arrangement.

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Most popular questions from this chapter

A shell-and-tube heat exchanger with 2-shell passes and 12 -tube passes is used to heat water \(\left(c_{p}=4180 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}\right)\) in the tubes from \(20^{\circ} \mathrm{C}\) to \(70^{\circ} \mathrm{C}\) at a rate of \(4.5 \mathrm{~kg} / \mathrm{s}\). Heat is supplied by hot oil \(\left(c_{p}=2300 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}\right)\) that enters the shell side at \(170^{\circ} \mathrm{C}\) at a rate of \(10 \mathrm{~kg} / \mathrm{s}\). For a tube-side overall heat transfer coefficient of \(350 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\), determine the heat transfer surface area on the tube side.

Hot water coming from the engine is to be cooled by ambient air in a car radiator. The aluminum tubes in which the water flows have a diameter of \(4 \mathrm{~cm}\) and negligible thickness. Fins are attached on the outer surface of the tubes in order to increase the heat transfer surface area on the air side. The heat transfer coefficients on the inner and outer surfaces are 2000 and \(150 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\), respectively. If the effective surface area on the finned side is 10 times the inner surface area, the overall heat transfer coefficient of this heat exchanger based on the inner surface area is (a) \(150 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\) (b) \(857 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\) (c) \(1075 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\) (d) \(2000 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\) (e) \(2150 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\)

A shell-and-tube heat exchanger is used for heating \(10 \mathrm{~kg} / \mathrm{s}\) of oil \(\left(c_{p}=2.0 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K}\right)\) from \(25^{\circ} \mathrm{C}\) to \(46^{\circ} \mathrm{C}\). The heat exchanger has 1 -shell pass and 6-tube passes. Water enters the shell side at \(80^{\circ} \mathrm{C}\) and leaves at \(60^{\circ} \mathrm{C}\). The overall heat transfer coefficient is estimated to be \(1000 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\). Calculate the rate of heat transfer and the heat transfer area.

Water is boiled at \(150^{\circ} \mathrm{C}\) in a boiler by hot exhaust gases \(\left(c_{p}=1.05 \mathrm{~kJ} / \mathrm{kg} \cdot{ }^{\circ} \mathrm{C}\right)\) that enter the boiler at \(400^{\circ} \mathrm{C}\) at a rate of \(0.4 \mathrm{~kg} / \mathrm{s}\) and leaves 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 (a) \(940 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\) (b) \(1056 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\) (c) \(1145 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\) (d) \(1230 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\) (e) \(1393 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\)

Oil in an engine is being cooled by air in a cross-flow heat exchanger, where both fluids are unmixed. Oil \(\left(c_{p h}=\right.\) \(2047 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}\) ) flowing with a flow rate of \(0.026 \mathrm{~kg} / \mathrm{s}\) enters the heat exchanger at \(75^{\circ} \mathrm{C}\), while air \(\left(c_{p c}=1007 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}\right)\) enters at \(30^{\circ} \mathrm{C}\) with a flow rate of \(0.21 \mathrm{~kg} / \mathrm{s}\). The overall heat transfer coefficient of the heat exchanger is \(53 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\) and the total surface area is \(1 \mathrm{~m}^{2}\). Determine \((a)\) the heat transfer effectiveness and \((b)\) the outlet temperature of the oil.

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