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Chapter 11: Problem 82

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

Short Answer

Expert verified
Answer: No, the temperature of the cold fluid cannot rise above the inlet temperature of the hot fluid at any location in a heat exchanger, as this would violate the Second Law of Thermodynamics.

Step by step solution

01

Understanding Heat Exchangers

A heat exchanger is a device used for transferring heat between two or more fluids, which can be either liquids, gases, or a combination of both. Heat exchangers are widely used in various industries, such as power generation, chemical processing, and HVAC systems. They are designed to efficiently transfer heat from one fluid to another, without the fluids coming into direct contact with each other.
02

Heat Transfer Principles

In a heat exchanger, heat transfer occurs through conduction and convection. Conduction is the transfer of heat through a solid or stationary fluid, while convection is the transfer of heat through a moving fluid. In simple terms, heat always flows from a region of higher temperature to a region of lower temperature, and it does so by means of these two mechanisms.
03

Analyzing the Temperature Situation

The question asks if the temperature of the cold fluid can rise above the inlet temperature of the hot fluid at any location in a heat exchanger. In other words, we need to determine if it's possible for the cold fluid to become hotter than the hot fluid's initial (inlet) temperature in a heat exchanging process.
04

Second Law of Thermodynamics

According to the Second Law of Thermodynamics, heat cannot spontaneously flow from a colder region to a hotter region. This means that, for the cold fluid to get hotter than the hot fluid's initial temperature, heat has to be transferred from the hot fluid to the cold fluid continuously along the length of the heat exchanger.
05

Answer and Explanation

However, as the cold fluid's temperature increases and approaches the hot fluid's inlet temperature, the temperature difference between the two fluids will decrease. Since the driving force behind heat transfer is the temperature difference between the fluids, the rate of heat transfer will also decrease as the temperature difference decreases. Consequently, it is impossible for the cold fluid's temperature to rise above the hot fluid's inlet temperature in a heat exchanger, as this would violate the Second Law of Thermodynamics.

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Most popular questions from this chapter

Consider a heat exchanger that has an NTU of \(0.1\). Someone proposes to triple the size of the heat exchanger and thus triple the NTU to \(0.3\) in order to increase the effectiveness of the heat exchanger and thus save energy. Would you support this proposal?

Hot exhaust gases of a stationary diesel engine are to be used to generate steam in an evaporator. Exhaust gases \(\left(c_{p}=1051 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}\right)\) enter the heat exchanger at \(550^{\circ} \mathrm{C}\) at a rate of \(0.25 \mathrm{~kg} / \mathrm{s}\) while water enters as saturated liquid and evaporates at \(200^{\circ} \mathrm{C}\left(h_{f g}=1941 \mathrm{~kJ} / \mathrm{kg}\right)\). The heat transfer surface area of the heat exchanger based on water side is \(0.5 \mathrm{~m}^{2}\) and overall heat transfer coefficient is \(1780 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\). Determine the rate of heat transfer, the exit temperature of exhaust gases, and the rate of evaporation of water.

A shell-and-tube heat exchanger with 2-shell passes and 4-tube passes is used for cooling oil \(\left(c_{p}=2.0 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K}\right)\) from \(125^{\circ} \mathrm{C}\) to \(55^{\circ} \mathrm{C}\). The coolant is water, which enters the shell side at \(25^{\circ} \mathrm{C}\) and leaves at \(46^{\circ} \mathrm{C}\). The overall heat transfer coefficient is \(900 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\). For an oil flow rate of \(10 \mathrm{~kg} / \mathrm{s}\), calculate the cooling water flow rate and the heat transfer area.

Air \(\left(c_{p}=1005 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}\right)\) enters a cross-flow heat exchanger at \(20^{\circ} \mathrm{C}\) at a rate of \(3 \mathrm{~kg} / \mathrm{s}\), where it is heated by a hot water stream \(\left(c_{p}=4190 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}\right)\) that enters the heat exchanger at \(70^{\circ} \mathrm{C}\) at a rate of \(1 \mathrm{~kg} / \mathrm{s}\). Determine the maximum heat transfer rate and the outlet temperatures of both fluids for that case.

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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