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Chapter 11: Problem 88

Consider two double-pipe counter-flow heat exchangers that are identical except that one is twice as long as the other one. Which heat exchanger is more likely to have a higher effectiveness?

Short Answer

Expert verified
And why? Answer: The heat exchanger that is twice as long as the other one is expected to have a higher effectiveness. This is because the longer heat exchanger provides a greater contact area between the two fluids, allowing for more heat transfer to occur, which results in higher effectiveness.

Step by step solution

01

Define effectiveness of a heat exchanger

In the context of heat exchangers, effectiveness is defined as the ratio between the actual amount of heat transfer and the maximum heat transfer possible. In other words, effectiveness quantifies how well the heat exchanger is performing, compared to an ideal situation. Higher effectiveness means better performance.
02

Understand the impact of heat exchanger length on effectiveness

In a double-pipe counter-flow heat exchanger, heat is transferred between two fluids flowing in opposite directions. The longer the heat exchanger, the more contact area between the flowing fluids, which leads to greater heat transfer. Thus, an increase in the length of a heat exchanger is expected to increase its effectiveness.
03

Compare the effectiveness of the two heat exchangers

We have two heat exchangers that are identical except for their lengths. One is twice as long as the other. Recall that the effectiveness of a heat exchanger increases with its length. So, the heat exchanger that is twice as long should have a higher effectiveness than the shorter one.
04

Conclusion

The heat exchanger that is twice as long as the other one is more likely to have a higher effectiveness. This is because the longer heat exchanger provides a greater contact area between the two fluids allowing for more heat transfer to occur, which results in higher effectiveness.

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Most popular questions from this chapter

Steam is to be condensed on the shell side of a 2-shell-passes and 8-tube- passes condenser, with 20 tubes in each pass. Cooling water enters the tubes 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) \(1.0\)

Under what conditions can a counter-flow heat exchanger have an effectiveness of one? What would your answer be for a parallel-flow heat exchanger?

In a chemical plant, a certain chemical is heated by hot water supplied by a natural gas furnace. The hot water \(\left(c_{p}=\right.\) \(4180 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K})\) is then discharged at \(60^{\circ} \mathrm{C}\) at a rate of \(8 \mathrm{~kg} / \mathrm{min}\). The plant operates \(8 \mathrm{~h}\) a day, 5 days a week, 52 weeks a year. The furnace has an efficiency of 78 percent, and the cost of the natural gas is \(\$ 1.00\) per therm ( 1 therm \(=105,500 \mathrm{~kJ})\). The average temperature of the cold water entering the furnace throughout the year is \(14^{\circ} \mathrm{C}\). In order to save energy, it is proposed to install a water-to-water heat exchanger to preheat the incoming cold water by the drained hot water. Assuming that the heat exchanger will recover 72 percent of the available heat in the hot water, determine the heat transfer rating of the heat exchanger that needs to be purchased and suggest a suitable type. Also, determine the amount of money this heat exchanger will save the company per year from natural gas savings.

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.

Can the temperature of the hot fluid drop below the inlet temperature of the cold fluid at any location in a heat exchanger? Explain.
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