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Chapter 11: Problem 78

What does the effectiveness of a heat exchanger represent? Can effectiveness be greater than one? On what factors does the effectiveness of a heat exchanger depend?

Short Answer

Expert verified
What factors impact the effectiveness of a heat exchanger? Answer: The effectiveness of a heat exchanger represents the ratio of the actual amount of heat transferred to the maximum possible amount of heat transfer under ideal conditions. It is a dimensionless number ranging from 0 to 1, and cannot be greater than one, as this would imply transferring more heat than theoretically possible. Factors affecting the effectiveness of a heat exchanger include material properties, heat exchanger design, fluid properties, temperature difference, and fouling.

Step by step solution

01

Definition of a Heat Exchanger

A heat exchanger is a device designed to transfer heat between two or more fluids without mixing them, allowing energy to be transferred from one fluid to another. This process is widely used in heating, cooling, and temperature regulation across various industries.
02

Concept of Effectiveness

The effectiveness of a heat exchanger represents the ratio of the actual amount of heat transferred by the exchanger to the maximum possible amount of heat that could be transferred under ideal conditions. It is a dimensionless number ranging from 0 to 1, with 0 indicating no heat transfer (ineffective) and 1 indicating maximum heat transfer (highly effective).
03

Limitations of Effectiveness

Effectiveness cannot be greater than one, as this would imply that the heat exchanger is transferring more heat than theoretically possible under ideal conditions. An effectiveness of 1 means that the heat exchanger is able to transfer all of the available heat from the hot fluid to the cold fluid, which in practical use would be an ideal scenario.
04

Factors Affecting Effectiveness

The effectiveness of a heat exchanger depends on various factors, including: 1. Material properties: The thermal conductivity of the materials used in the construction of the heat exchanger plays a vital role in heat transfer efficiency. 2. Heat exchanger design: The type and configuration of the heat exchanger, such as plate, shell and tube, or air-to-air, impacts effectiveness due to variations in heat transfer coefficients and surface area. 3. Fluid properties: The specific heat capacity and flow rates of the fluids being exchanged affect the amount of heat that can be transferred. 4. Temperature difference: The greater the temperature difference between the two fluids, the more heat can be potentially transferred, leading to a higher effectiveness. 5. Fouling: The buildup of deposits on the heat transfer surfaces can reduce the overall heat transfer efficiency and reduce effectiveness over time.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Heat Transfer Fundamentals
Heat transfer is a fundamental concept in thermodynamics that involves the movement of thermal energy from one place to another and is essential in designing efficient heat exchangers. There are three primary modes of heat transfer: conduction, which is the transfer of heat through a solid; convection, which is the movement of heat by the flow of liquids or gases; and radiation, which is heat transfer through electromagnetic waves.

Understanding these modes is crucial because they influence how heat exchangers are designed and how effectively they operate. The effectiveness of a heat exchanger greatly depends on optimizing these heat transfer modes to ensure maximum energy transfer between fluids without allowing them to mix.
Maximum Heat Transfer
Maximum heat transfer in a heat exchanger is the ideal amount of thermal energy that can be exchanged between fluids, determined by the specific heat capacity, flow rates, and the temperature difference between the two fluids. It represents an upper limit under perfect conditions, which in reality is not achievable due to practical limitations like material resistance to heat flow and friction losses.

However, aiming for maximum heat transfer efficiency leads to better design choices. For instance, increasing the surface area in contact between the hot and cold fluids can enhance heat transfer rates, as can selecting materials with higher thermal conductivity for the heat exchanger's construction.
Heat Exchanger Design
The design of a heat exchanger is paramount to its effectiveness. Engineers must choose from various configurations such as shell-and-tube, plate, or air-to-air, each with their unique advantages and constraints. The design dictates the heat transfer area, flow path, pressure drops, and overall size of the unit.

A well-designed heat exchanger provides sufficient surface area for heat exchange, promotes turbulent flow to enhance heat transfer coefficients, and minimizes fouling. Further improvements in design can often be accomplished by incorporating features like corrugated plates or baffles to disrupt laminar flow, which increases the heat transfer rate.
Thermal Conductivity
Thermal conductivity is a measure of a material's ability to conduct heat. Materials with high thermal conductivity, such as copper or aluminum, are typically used in heat exchanger construction to facilitate the transfer of heat between the fluids. In contrast, materials with low thermal conductivity act as insulators and are not suitable for the heat transferring components of heat exchangers.

Selecting materials with the appropriate thermal conductivity is crucial because it directly affects the efficiency of heat transfer. A higher thermal conductivity means that heat can travel through the material more rapidly, resulting in higher effectiveness of the heat exchanger.
Temperature Difference in Heat Exchangers
The temperature difference between the hot and cold fluids in a heat exchanger is a critical factor impacting effectiveness. A larger temperature gradient provides a higher driving force for heat transfer, typically leading to increased efficiency. The relationship between temperature difference and heat transferred is described by the Log Mean Temperature Difference (LMTD) method in steady-state heat exchange situations.

Understanding the impact of temperature difference on heat exchanger performance is essential when designing and operating these systems, as it helps in estimating the potential transfer of energy and sizing the heat exchanger accordingly to meet the required thermal duties.

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Most popular questions from this chapter

Consider a recuperative cross flow heat exchanger (both fluids unmixed) used in a gas turbine system that carries the exhaust gases at a flow rate of \(7.5 \mathrm{~kg} / \mathrm{s}\) and a temperature of \(500^{\circ} \mathrm{C}\). The air initially at \(30^{\circ} \mathrm{C}\) and flowing at a rate of \(15 \mathrm{~kg} / \mathrm{s}\) is to be heated in the recuperator. The convective heat transfer coefficients on the exhaust gas and air side are \(750 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\) and \(300 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\), respectively. Due to long term use of the gas turbine the recuperative heat exchanger is subject to fouling on both gas and air side that offers a resistance of \(0.0004 \mathrm{~m}^{2} \cdot \mathrm{K} / \mathrm{W}\) each. Take the properties of exhaust gas to be the same as that of air \(\left(c_{p}=1069 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}\right)\). If the exit temperature of the exhaust gas is \(320^{\circ} \mathrm{C}\) determine \((a)\) if the air could be heated to a temperature of \(150^{\circ} \mathrm{C}(b)\) the area of heat exchanger \((c)\) if the answer to part (a) is no, then determine what should be the air mass flow rate in order to attain the desired exit temperature of \(150^{\circ} \mathrm{C}\) and \((d)\) plot variation of the exit air temperature over a temperature range of \(75^{\circ} \mathrm{C}\) to \(300^{\circ} \mathrm{C}\) with air mass flow rate assuming all the other conditions remain the same.

A counter-flow heat exchanger is stated to have an overall heat transfer coefficient of \(284 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\) when operating at design and clean conditions. Hot fluid enters the tube side at \(93^{\circ} \mathrm{C}\) and exits at \(71^{\circ} \mathrm{C}\), while cold fluid enters the shell side at \(27^{\circ} \mathrm{C}\) and exits at \(38^{\circ} \mathrm{C}\). After a period of use, built-up scale in the heat exchanger gives a fouling factor of \(0.0004 \mathrm{~m}^{2} \cdot \mathrm{K} / \mathrm{W}\). If the surface area is \(93 \mathrm{~m}^{2}\), determine \((a)\) the rate of heat transfer in the heat exchanger and \((b)\) the mass flow rates of both hot and cold fluids. Assume both hot and cold fluids have a specific heat of \(4.2 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K}\).

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.

How is the thermal resistance due to fouling in a heat exchanger accounted for? How do the fluid velocity and temperature affect fouling?

Consider a double-pipe parallel-flow heat exchanger of length \(L\) The inner and outer diameters of the inner tube are \(D_{1}\) and \(D_{2}\), respectively, and the inner diameter of the outer tube is \(D_{3}\). Explain how you would determine the two heat transfer surface areas \(A_{i}\) and \(A_{o}\). When is it reasonable to assume \(A_{i} \approx A_{o} \approx A_{s}\) ?
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