Radiation Heat Transfer
M Zhang and David P DeWitt
Woodruff School of Mechanical Engineering Georgia Institute of Technology
DK2204_book.fm Page xv Monday, October 20, 2008 2:15 PM www.elsolucionario.net www.elsolucionario.net
DK2204_book.fm Page xvi Monday, October 20, 2008 2:15 PM www.elsolucionario.net www.elsolucionario.net
1.2 Thermodynamic Properties of Pure Fluids 3
1.2.1 Importance of Pure-Fluid Properties 3
1.2.2 Relative Importance of Different Properties 3
1.2.4 Pure Fluids with Reference-Quality Data 5
1.2.5 Pure Fluids with Moderate Amounts of Data 5
1.2.6 Pure Fluids with Little or No Data 7
1.2.8 Critical Constants and Acentric Factors for Pure Fluids 8
1.3 Thermodynamic Properties of Single-Phase Mixtures 8
1.4.1 Types of Phase-Equilibrium Calculations 10
1.5.1 Kinetic Theory for Transport Properties 14
1.6.1 Vapor-Liquid Equilibria and Activity Coefficients 17
1.7 Properties for Chemical Reaction Equilibria 20
1.8 Measurement of Fluid Thermophysical Properties 20
1.8.4 Heat Capacity and Caloric Properties 22
DK2204_book.fm Page 1 Monday, October 20, 2008 2:15 PM www.elsolucionario.net www.elsolucionario.net
1.9 Overview of Major Data Sources 27
Due to the vast array of physical and chemical property data required by engineers, no single handbook can encompass all necessary information Consequently, this chapter focuses on directing readers to trustworthy data sources and providing methods for data extrapolation, estimation, or measurement, rather than including extensive tables of data.
The quality of data is crucial, as much information found in handbooks, online, and in scientific journals can be inaccurate due to various factors such as experimental errors, measurement processing mistakes, or simple copying errors Responsible engineers must prioritize obtaining reliable data rather than just any number Achieving trustworthy physical and chemical property data requires thorough evaluation, which includes expert analysis of experimental methods, consistency checks, comparisons across multiple datasets, and consideration of trends within chemical families It is advisable to use sources that provide evaluated data with indications of quality.
Uncertainty significantly impacts the value of data, as it is crucial to know whether the uncertainty is 1% or 100% Ideally, all data should include a quantitative measure of uncertainty that can be integrated into engineering design calculations However, in reality, we often rely on approximate or qualitative estimates of these uncertainties The more information we can provide about uncertainty, the more reliable our data becomes.
Data sources vary widely in cost, from free options to those priced in the thousands While engineers aim to minimize expenses, it's crucial to remember that "you get what you pay for." Free data from government or academic sources may be tempting, but reliable information typically comes at a cost due to the skilled labor involved in data collection and evaluation Relying on questionable free data for critical multimillion-dollar designs is unwise when more trustworthy alternatives are available at a reasonable price.
As process simulation programs gain popularity among engineers, many tend to view their thermodynamic calculations as a "black box," overlooking the importance of the underlying data and models While developers of these simulators have invested significant effort in validating both data and models, it is crucial for users not to place blind trust in the results simply because they are generated by these tools.
DK2204_book.fm Page 2 Monday, October 20, 2008 2:15 PM www.elsolucionario.net www.elsolucionario.net
Understanding the physical and chemical properties is crucial for effective process simulation, as even the best software can yield inaccurate results if unsuitable thermodynamic methods and data are applied This chapter aims to equip readers with the necessary resources to make informed decisions regarding the selection of models and data in process simulation, ensuring they can effectively supplement software when essential data is lacking.
Before proceeding, we mention sources for a few areas not covered in this chapter Basic chemical thermodynamics is the subject of Chapter 4 For polymers and their solutions, the
The Polymer Handbook is an essential reference for polymer thermophysical properties, complemented by two AIChE DIPPR project books For estimating properties of mixtures represented by distillation curves, particularly in petroleum fractions, the API Technical Data Book provides valuable insights Additionally, the NIST Chemistry database offers a comprehensive collection of molecular data, including dipole moments and spectroscopic constants.
1.2 THERMODYNAMIC PROPERTIES OF PURE FLUIDS
1.2.1 I MPORTANCE OF P URE -F LUID P ROPERTIES
Chemical engineers must understand pure-fluid properties for several key reasons Firstly, many industrial processes utilize fluids that are nearly pure, such as water and steam, where pure-fluid properties are adequate Secondly, the behavior of pure fluids can serve as a useful approximation for modeling mixtures of similar compounds, often simplifying complex calculations Lastly, and most crucially, accurate pure-component data is essential, as most thermophysical property models for mixtures are based on the properties of these pure components.
1.2.2 R ELATIVE I MPORTANCE OF D IFFERENT P ROPERTIES
In chemical engineering, vapor pressure is frequently the most critical property of pure fluids due to its significant role in separation processes reliant on vapor-liquid equilibria Additionally, understanding vapor pressure is essential for addressing safety and environmental issues related to fluid volatility.
Because energy usage and heat transfer are important in process operations, caloric properties
(enthalpy, heat capacity) can be considered the second most important area The enthalpy of vaporization is particularly important in vapor-liquid separations.
Volumetric properties, including density and isothermal compressibility, play a crucial role in various process calculations Fortunately, measuring and predicting fluid densities with adequate accuracy is typically straightforward for most applications.
Other properties of interest include surface tension and transport properties (viscosity, thermal conductivity, diffusivity) Transport properties will be covered in a later section.
Water is essential in its pure or nearly pure form, serving as both a process stream and a heat-transfer fluid, such as cooling water or steam Due to its critical role, international standards for water's thermophysical properties have been established by the International Association for the Properties of Water and Steam (IAPWS) For more information, visit www.iapws.org.
Historically, engineers relied on "steam tables" to access the properties of water and steam; although these resources still exist, modern software that utilizes IAPWS property standards is now more commonly used for convenience Table 1.1 provides essential thermodynamic properties for saturated liquid and vapor, serving as a quick reference, while design calculations typically necessitate more comprehensive tables or software solutions.
DK2204_book.fm Page 3 Monday, October 20, 2008 2:15 PM www.elsolucionario.net www.elsolucionario.net
TABLE 1.1 Thermodynamic Properties of Saturated Water and Steam as a Function of Temperature
Density, kg/m 3 Enthalpy, kJ/kg Entropy, kJ/(kgãK)
DK2204_book.fm Page 4 Monday, October 20, 2008 2:15 PM www.elsolucionario.net www.elsolucionario.net
1.2.4 P URE F LUIDS WITH R EFERENCE -Q UALITY D ATA
Certain chemicals are crucial due to their industrial significance, notably the primary components of air, light hydrocarbons, and common refrigerants Accurate measurements of their properties across various temperatures and pressures have led to the creation of reliable equations of state (EOS) These EOS enable precise calculations of thermodynamic properties for pure fluids, adhering closely to the original data's uncertainty Therefore, when an EOS is available for a fluid, it is the preferred source of data.
Reference-quality EOS typically have a complicated functional form, with many parameters.
Software is available that implements equations of state (EOS) for various fluids, with the NIST database providing formulations for around 80 pure fluids Additionally, a portion of this data can be accessed through the NIST Chemistry Webbook.
1.2.5 P URE F LUIDS WITH M ODERATE A MOUNTS OF D ATA
Many other substances have insufficient data for a reference-quality EOS There may be a few vapor-pressure data, and perhaps some other measurements such as liquid density or heat capacity.
In such cases, there are two basic approaches.
The first approach involves simple correlations of properties, which is particularly effective when the property of interest depends solely on one variable, like vapor pressure as a function of temperature This method is also applicable to liquid-phase properties, provided they are not near the critical point, as these properties typically show minimal sensitivity to pressure and can be effectively represented as functions of temperature alone Several databases support this analysis.
[11–14] contain correlations for pure-fluid properties as a function of temperature for many common substances, and vapor-pressure correlations for many substances are in some additional sources [5,
15] It is important to be aware of the range of conditions in which a correlation has been fitted, as extrapolation can lead to significant errors.