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

An air-cooled condenser is used to condense isobutane in a binary geothermal power plant. The isobutane is condensed at \(85^{\circ} \mathrm{C}\) by air \(\left(c_{p}=1.0 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K}\right)\) that enters at \(22^{\circ} \mathrm{C}\) at a rate of \(18 \mathrm{~kg} / \mathrm{s}\). The overall heat transfer coefficient and the surface area for this heat exchanger are \(2.4 \mathrm{~kW} / \mathrm{m}^{2} \cdot \mathrm{K}\) and \(1.25 \mathrm{~m}^{2}\), respectively. The outlet temperature of air is (a) \(45.4^{\circ} \mathrm{C}\) (b) \(40.9^{\circ} \mathrm{C}\) (c) \(37.5^{\circ} \mathrm{C}\) (d) \(34.2^{\circ} \mathrm{C}\) (e) \(31.7^{\circ} \mathrm{C}\)

There are two heat exchangers that can meet the heat transfer requirements of a facility. One is smaller and cheaper but requires a larger pump, while the other is larger and more expensive but has a smaller pressure drop and thus requires a smaller pump. Both heat exchangers have the same life expectancy and meet all other requirements. Explain which heat exchanger you would choose and under what conditions.

Consider an oil-to-oil double-pipe heat exchanger whose flow arrangement is not known. The temperature measurements indicate that the cold oil enters at \(20^{\circ} \mathrm{C}\) and leaves at \(55^{\circ} \mathrm{C}\), while the hot oil enters at \(80^{\circ} \mathrm{C}\) and leaves at \(45^{\circ} \mathrm{C}\). Do you think this is a parallel-flow or counter-flow heat exchanger? Why? Assuming the mass flow rates of both fluids to be identical, determine the effectiveness of this heat exchanger.

A shell-and-tube heat exchanger with 2-shell passes and 8 -tube passes is used to heat ethyl alcohol \(\left(c_{p}=2670 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}\right)\) in the tubes from \(25^{\circ} \mathrm{C}\) to \(70^{\circ} \mathrm{C}\) at a rate of \(2.1 \mathrm{~kg} / \mathrm{s}\). The heating is to be done by water \(\left(c_{p}=\right.\) \(4190 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K})\) that enters the shell at \(95^{\circ} \mathrm{C}\) and leaves at \(60^{\circ} \mathrm{C}\). If the overall heat transfer coefficient is \(800 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\), determine the heat transfer surface area of the heat exchanger using \((a)\) the LMTD method and \((b)\) the \(\varepsilon-\mathrm{NTU}\) method.

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.

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