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Chapter 11: Problem 87

Consider a shell-and-tube water-to-water heat exchanger with identical mass flow rates for both the hotand cold-water streams. Now the mass flow rate of the cold water is reduced by half. Will the effectiveness of this heat exchanger increase, decrease, or remain the same as a result of this modification? Explain. Assume the overall heat transfer coefficient and the inlet temperatures remain the same.

Short Answer

Expert verified
Answer: The effectiveness of the heat exchanger will decrease when the mass flow rate of the cold water is reduced by half, while keeping the overall heat transfer coefficient and inlet temperatures the same.

Step by step solution

01

Define heat exchanger effectiveness

The effectiveness of a heat exchanger (ε) is a measure of how well it transfers heat between the hot and cold fluids. It is defined as the ratio of the actual heat transfer rate (Q) to the maximum possible heat transfer rate (Q_max): ε = \frac{Q}{Q_{max}}
02

Determine the heat transfer rates

The actual heat transfer rate (Q) in a heat exchanger can be calculated based on the mass flow rate (m), specific heat capacity (c_p), and inlet and outlet temperature differences: Q = m c_p ΔT The maximum possible heat transfer rate (Q_max) occurs when the cold fluid reaches the inlet temperature of the hot fluid. In this case, the temperature difference between the hot and cold fluids would be the largest possible: Q_{max} = m c_p ΔT_{max}
03

Consider the effect of reducing the cold water mass flow rate

Now, let's consider the effect of reducing the mass flow rate of the cold water by half. As the mass flow rate of cold water is reduced, the amount of heat transfer between the two fluids will also decrease. However, since the mass flow rate of the hot water remains constant, the maximum possible heat transfer rate (Q_max) will not change.
04

Analyze the heat exchanger effectiveness

As the mass flow rate of the cold water decreases, the ratio of the actual heat transfer rate (Q) to the maximum possible heat transfer rate (Q_max) will also decrease: ε = \frac{Q}{Q_{max}} =\frac{ mc_p ΔT}{ mc_p ΔT_{max}} Since the mass flow rate (m) decreases and the other values (c_p, ΔT, and ΔT_{max}) remain constant, the effectiveness (ε) of the heat exchanger will decrease as a result of reducing the cold water mass flow rate by half. In conclusion, the effectiveness of the shell-and-tube water-to-water heat exchanger will decrease when the mass flow rate of the cold water is reduced by half, while keeping the overall heat transfer coefficient and inlet temperatures the same.

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Most popular questions from this chapter

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.

Oil is being cooled from \(180^{\circ} \mathrm{F}\) to \(120^{\circ} \mathrm{F}\) in a 1 -shell and 2-tube heat exchanger with an overall heat transfer coefficient of \(40 \mathrm{Btu} / \mathrm{h} \mathrm{ft} 2{ }^{\circ} \mathrm{F}\). Water \(\left(c_{p c}=1.0 \mathrm{Btu} / \mathrm{lbm} \cdot{ }^{\circ} \mathrm{F}\right)\) enters at \(80^{\circ} \mathrm{F}\) and exits at \(100^{\circ} \mathrm{F}\) with a mass flow rate of \(20,000 \mathrm{lbm} / \mathrm{h}\), determine (a) the log mean temperature difference and \((b)\) the surface area of the heat exchanger.

Consider the flow of saturated steam at \(270.1 \mathrm{kPa}\) that flows through the shell side of a shell-and-tube heat exchanger while the water flows through 4 tubes of diameter \(1.25 \mathrm{~cm}\) at a rate of \(0.25 \mathrm{~kg} / \mathrm{s}\) through each tube. The water enters the tubes of heat exchanger at \(20^{\circ} \mathrm{C}\) and exits at \(60^{\circ} \mathrm{C}\). Due to the heat exchange with the cold fluid, steam is condensed on the tubes external surface. The convection heat transfer coefficient on the steam side is \(1500 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\), while the fouling resistance for the steam and water may be taken as \(0.00015\) and \(0.0001 \mathrm{~m}^{2} \cdot \mathrm{K} / \mathrm{W}\), respectively. Using the NTU method, determine \((a)\) effectiveness of the heat exchanger, \((b)\) length of the tube, and \((c)\) rate of steam condensation.

In a textile manufacturing plant, the waste dyeing water \(\left(c_{p}=4295 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}\right)\) at \(75^{\circ} \mathrm{C}\) is to be used to preheat fresh water \(\left(c_{p}=4180 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}\right)\) at \(15^{\circ} \mathrm{C}\) at the same flow rate in a double-pipe counter-flow heat exchanger. The heat transfer surface area of the heat exchanger is \(1.65 \mathrm{~m}^{2}\) and the overall heat transfer coefficient is \(625 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\). If the rate of heat transfer in the heat exchanger is \(35 \mathrm{~kW}\), determine the outlet temperature and the mass flow rate of each fluid stream.

Saturated liquid benzene flowing at a rate of \(5 \mathrm{~kg} / \mathrm{s}\) is to be cooled from \(75^{\circ} \mathrm{C}\) to \(45^{\circ} \mathrm{C}\) by using a source of cold water \(\left(c_{p}=4187 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}\right)\) flowing at \(3.5 \mathrm{~kg} / \mathrm{s}\) and \(15^{\circ} \mathrm{C}\) through a \(20-\mathrm{mm}-\) diameter tube of negligible wall thickness. The overall heat transfer coefficient of the heat exchanger is estimated to be \(750 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\). If the specific heat of the liquid benzene is \(1839 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}\) and assuming that the capacity ratio and effectiveness remain the same, determine the heat exchanger surface area for the following four heat exchangers: \((a)\) parallel flow, \((b)\) counter flow, \((c)\) shelland-tube heat exchanger with 2 -shell passes and 40-tube passes, and \((d)\) cross-flow heat exchanger with one fluid mixed (liquid benzene) and other fluid unmixed (water).
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