/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 29 What are the common approximatio... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 11: Problem 29

What are the common approximations made in the analysis of heat exchangers?

Short Answer

Expert verified
Answer: The common approximations made in analyzing heat exchangers include assuming constant fluid properties, neglecting heat transfer to surroundings, assuming steady-state operation, assuming uniform temperature distribution, and using simplified correlations for heat transfer coefficients and pressure drops. These approximations are used to simplify the calculations and make the design process more straightforward. While they may not always provide highly accurate results, they are generally considered acceptable for design and optimization purposes.

Step by step solution

01

1. Constant properties assumption

One of the common approximations made in analyzing heat exchangers is assuming that the physical properties of the fluids involved, such as specific heat, density, viscosity, and thermal conductivity, are constant. In reality, these fluid properties may change with temperature; however, assuming constant properties can simplify the calculations and is considered valid for small temperature differences.
02

2. Neglecting heat transfer to the surroundings

Another common approximation is to assume that there is no heat transfer to or from the surroundings. In reality, a heat exchanger may lose or gain heat to its surroundings, depending on the environment. However, this heat transfer can often be neglected in the analysis since it is usually small compared to the heat being transferred between the fluids.
03

3. Steady-state operation

In many heat exchanger analyses, it is assumed that the system is operating under steady-state conditions. This means that the temperatures, flow rates, and other variables are not changing with time. In practice, there may be transient periods where conditions are changing, but steady-state analysis is often sufficient for design and optimization purposes.
04

4. Uniform temperature distribution

In some heat exchanger analyses, it is assumed that the temperature distribution within a fluid is uniform. This means that the temperature is the same throughout the fluid at any given location in the heat exchanger. In reality, the temperature can vary across the fluid for various reasons, such as the presence of temperature gradients. However, assuming a uniform temperature distribution simplifies calculations and can be an acceptable approximation in many cases.
05

5. Simplified heat transfer correlations

In the analysis of heat exchangers, many simplified correlations are used to predict heat transfer coefficients and pressure drops. These correlations may not always provide highly accurate results, but they are generally useful in providing reasonable estimates for heat transfer performance and sizing calculations. In conclusion, various common approximations are made in the analysis of heat exchangers to simplify the calculations and make the design process more straightforward. These assumptions include constant fluid properties, neglecting heat transfer to surroundings, assuming steady-state operation, uniform temperature distribution, and using simplified correlations for heat transfer coefficients and pressure drops. While these approximations may not always provide highly accurate results, they are generally considered acceptable for design and optimization purposes.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Constant Properties Assumption
In the world of heat exchangers, the properties of a fluid, like its specific heat, density, viscosity, and thermal conductivity, can vary with temperature.

However, to simplify calculations, we often assume these properties remain constant. This approach, while not entirely accurate, allows engineers to streamline the analysis significantly.

For small temperature differences, this approximation can be quite valid as the changes in properties are minimal. In engineering, simplicity is key, and a constant properties assumption often provides a good balance between simplicity and accuracy.
Steady-State Operation
Heat exchangers are frequently analyzed under the assumption of steady-state operation. This means that the variables such as temperatures and flow rates remain unchanged over time.

In practical scenarios, conditions may fluctuate, especially during startup or shutdown phases. However, most industrial processes aim for a steady operational state as it makes the system easier to manage and optimize.

The assumption of steady-state operation is crucial as it allows designers to focus on achieving consistent performance, simplifying both design and analysis.
Uniform Temperature Distribution
Within a heat exchanger, assuming a uniform temperature distribution means believing that the temperature of a fluid is consistent at any point within the system.

Reality often differs as various factors, such as fluid mixing and flow patterns, can lead to temperature gradients.

However, for many practical purposes, especially those involving small scales or short lengths, this assumption helps simplify complex analysis.

It provides a solid foundation for modeling heat exchange without delving into the intricate details of fluid dynamics.
Neglecting Heat Transfer to Surroundings
When analyzing heat exchangers, it's common to overlook any heat exchange with the surroundings.

This assumption stems from the idea that the primary heat transfer happens between the fluids within the equipment, and any environmental heat loss or gain is negligible.

In many cases, this is true since insulation and system designs are optimized to minimize such interactions. By ignoring these small exchanges, we can simplify calculations while maintaining reasonable accuracy in our analysis.
Heat Transfer Coefficients
To predict how efficiently a heat exchanger performs, engineers rely on heat transfer coefficients. These coefficients are often calculated using simplified correlations derived from experiments and theory.

Though these correlations may not provide pinpoint accuracy, they offer useful estimates essential for preliminary design and system sizing.

Understanding these coefficients and the assumptions behind their calculations is crucial for engineering students and professionals as they allow a balance between complexity and computational ease, optimizing time and resources in the design process.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

An air handler is a large unmixed heat exchanger used for comfort control in large buildings. In one such application, chilled water \(\left(c_{p}=4.2 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K}\right)\) enters an air handler at \(5^{\circ} \mathrm{C}\) and leaves at \(12^{\circ} \mathrm{C}\) with a flow rate of \(1000 \mathrm{~kg} / \mathrm{h}\). This cold water cools air \(\left(c_{p}=1.0 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K}\right)\) from \(25^{\circ} \mathrm{C}\) to \(15^{\circ} \mathrm{C}\). The rate of heat transfer between the two streams is (a) \(8.2 \mathrm{~kW}\) (b) \(23.7 \mathrm{~kW}\) (c) \(33.8 \mathrm{~kW}\) (d) \(44.8 \mathrm{~kW}\) (e) \(52.8 \mathrm{~kW}\)

By taking the limit as \(\Delta T_{2} \rightarrow \Delta T_{1}\), show that when \(\Delta T_{1}=\Delta T_{2}\) for a heat exchanger, the \(\Delta T_{\mathrm{lm}}\) relation reduces to \(\Delta T_{\mathrm{lm}}=\Delta T_{1}=\Delta T_{2} .\)

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

Explain how the maximum possible heat transfer rate \(\dot{Q}_{\max }\) in a heat exchanger can be determined when the mass flow rates, specific heats, and the inlet temperatures of the two fluids are specified. Does the value of \(\dot{Q}_{\max }\) depend on the type of the heat exchanger?

A shell-and-tube heat exchanger is used for heating \(10 \mathrm{~kg} / \mathrm{s}\) of oil \(\left(c_{p}=2.0 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K}\right)\) from \(25^{\circ} \mathrm{C}\) to \(46^{\circ} \mathrm{C}\). The heat exchanger has 1 -shell pass and 6-tube passes. Water enters the shell side at \(80^{\circ} \mathrm{C}\) and leaves at \(60^{\circ} \mathrm{C}\). The overall heat transfer coefficient is estimated to be \(1000 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\). Calculate the rate of heat transfer and the heat transfer area.
See all solutions

Recommended explanations on Physics Textbooks

Linear Momentum

Read Explanation

Conservation of Energy and Momentum

Read Explanation

Engineering Physics

Read Explanation

Electromagnetism

Read Explanation

Physics of Motion

Read Explanation

Further Mechanics and Thermal Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.