Energy Transfers by Radiation - Abdelhanine Benallou - ebook

Energy Transfers by Radiation ebook

Abdelhanine Benallou

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Inside industrial furnaces and combustion chambers, energy is essentially exchanged by radiation. It is through the same mechanism that the energy emitted by the Sun spreads through different media to reach the Earth. Developing a sound understanding of the laws underlying energy exchanges by radiation is therefore essential, not only for establishing design equations for industrial equipment, but also for an optimal harvesting of solar energy and a better understanding of climate change phenomena such as the greenhouse effect. Energy Transfers by Radiation establishes the basic laws and equations which support the quantification of energy fluxes transferred between surfaces for situations similar to those usually encountered in industrial processes or in solar energy applications.

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Table of Contents

Cover

Preface

Introduction

1 Origin of Radiation

1.1. Introduction

1.2. The Niels Bohr model

1.3. Nature of the radiating energy

2 Magnitudes Used in Radiation

2.1. Introduction

2.2. Monochromatic, total, directional and hemispherical magnitudes

2.3. Absorption, reflection and transmission

2.4. Total intensity of a source in one direction

2.5. Total luminance of a source in one direction

2.6. Illuminance of a receiving surface

2.7. Examples of monochromatic magnitudes and explanation of the greenhouse effect

2.8. Relations between magnitudes

3 Analysis of Radiative Energy Transfers: Black-body Radiation

3.1. Introduction

3.2. Definition of a black body

3.3. Physical creation of the black body

3.4. Black-body radiation

4 Radiant Properties of Real Surfaces

4.1. Introduction

4.2. Emissivity of a real surface

4.3. Gray body

4.4. Effective temperature of a real surface

4.5. Luminance of a real surface

4.6. Kirchhoff’s law

5 Radiation Balances between Real Surfaces Separated by a Transparent Medium

5.1. Introduction

5.2. The angle factor

5.3. Expressing the shape factor

5.4. Relations between shape factors

5.5. Reducing the number of shape factors to be calculated

5.6. Superposition principle

5.7. Crossed-string method: very long surfaces

6 Practical Determination of Shape Factors

6.1. Introduction

6.2. Methods of practical determination of shape factors

6.3. Shape factors for standard geometric configurations

7 Balances of Radiative Energy Transfers between Black Surfaces

7.1. Introduction

7.2. Establishing balance equations

7.3. Solving radiation balances for black surfaces

8 Balances on Radiative Energy Transfers between Gray Surfaces

8.1. Introduction

8.2. Reminder of the radiative properties of real surfaces

8.3. Radiosity

8.4. Balances on gray surfaces

8.5. Solving the radiation balance equations between gray surfaces

9 Electrical Analogies in Radiation

9.1. Introduction

9.2. Analogies for black surfaces

9.3. Electrical analogies for heat transfer between gray surfaces

9.4. Gray shape factor

9.5. Illustration: gray shape factor of the industrial furnace with adiabatic walls

10 Reduction of Radiating Energy Transfers through Filtering

10.1. Introduction

10.2. Expressing the flux density for a filterless transfer

10.3. Reducing the flux through filtering

10.4. Comparing

q

0

and

q

m

10.5. Scenario where plates

S

0

and

S

n

have the same emissivity

11 Radiative Energy Transfers in Semi-transparent Media

11.1. Introduction

11.2. Radiation in semi-transparent gases

11.3. Illustration: calculating the flux radiated by combustion gases

11.4. Reading: discovery of the Stefan-Boltzmann law

12 Exercises and Solutions

EXERCISE 12.1. Lithium vapor lamps

EXERCISE 12.2. Mercury vapor lamps

EXERCISE 12.3. Radiating transfer between two surfaces

EXERCISE 12.4. Expression of ϕ

1

EXERCISE 12.5. Black body

EXERCISE 12.6. Calculating the emittances of a black surface at different temperatures

EXERCISE 12.7. Luminance of a black body

EXERCISE 12.8. Balances of radiative energy transfers between black surfaces

EXERCISE 12.9. Balance of radiative energy transfers between a gray surface and a black surface

EXERCISE 12.10. Effective temperature of a gray surface

EXERCISE 12.11. Surfaces under total influence

EXERCISE 12.12. Expressing the solid angle

EXERCISE 12.13. Asymptotic form of Planck's law for short wavelengths

EXERCISE 12.14. Asymptotic form of Planck's law for large wavelengths

EXERCISE 12.15. Calculating the Sun’s temperature from its spectral profile

EXERCISE 12.16. Determining the wavelength corresponding to a star’s maximum intensity

EXERCISE 12.17. Comparison of energies radiated in different bands

EXERCISE 12.18. Calculating the luminance of a black surface

EXERCISE 12.19. Heat transfer between two gray, opaque surfaces

EXERCISE 12.20. Illuminance of the Earth from the Sun

EXERCISE 12.21. Lighting a parallelepiped-shaped room

EXERCISE 12.22. Radiation between a hot source and a wall

EXERCISE 12.23. Cables with parallel axes

EXERCISE 12.24. Elementary surface perpendicular to a rectangle

EXERCISE 12.25. Parallel planes, centered on an axis, with the same surface area

EXERCISE 12.26. Two parallel bands of different widths

EXERCISE 12.27. Two cylinders with parallel axes

EXERCISE 12.28. Two rectangular perpendicular planes with a side in common

EXERCISE 12.29. Shape factors of complementary surfaces

EXERCISE 12.30. Lighting via the corner of a ceiling

EXERCISE 12.31. Optimizing the location of a bay window

EXERCISE 12.32. Lighting a conference room using a luminous disc

EXERCISE 12.33. Luminous flux of a public lighting point

EXERCISE 12.34. Heating of an outdoor dining area

EXERCISE 12.35. Radiation inside a cold room

EXERCISE 12.36. Reducing heat exchanges using a filter

EXERCISE 12.37. Reducing radiative transfer through filtration

EXERCISE 12.38. Calculating the solar radiation received on the ground

Appendix: Database

A.1. Introduction

A.2. Densities

A.3. Heat capacities

A.4. Heat conductivities

A.5. Data on heat insulation materials

A.6. Physical properties of water

A.7. Physical properties of air

A.8. ω

1

values for the analytical solution of heat equations

A.9. Values of A

ω1

A.10. Γ function

A.11. Bessel functions

A.12. Physical properties of nanofluids

A.13. Physical properties of molten salts

A.14. Physical properties of liquid metals

A.15. Emissivities

A.16. Emittance fractions in a given wavelength band

A.17. Unit conversion tables

A.18. Fundamental constants

References

Index

End User License Agreement

List of Tables

Chapter 1

Table 1.1. The different regions of the electromagnetic spectrum

Chapter 3

Table 3.1. Calculation of values of λm for temperatures between 300 and 5,500 K.

Table 3.2. Values of λ T for infrared band boundaries

Table 3.3. Fractions f01 and f02 of the energies emitted (in %) and calculation ...

Table 3.4. Fractions, f0, λ1, emitted at different values of λT

Table 3.5. Fractions, f0, λ2, emitted at different values of λT

Chapter 4

Table 4.1. Total emissivities of several materials

Chapter 6

Table 6.1. Calculating F12

Table 6.2. F12 as a function of and α

Chapter 7

Table 7.1. Equilibrium temperatures of the baking oven

Table 7.2. Calculations of the different fluxes

Table 7.3. Results

Chapter 12

Table 12.1. What does ϕ12 represent?

Table 12.2. Solution

Table 12.3. Choice of answers

Table 12.4. Solution

Table 12.5. Which answers apply to a black body?

Table 12.6. Solution

Table 12.7. What are the true properties for a black body?

Table 12.8. Properties that are true for a black body

Table 12.9. Wavelengths considered

Table 12.10. Monochromatic emittances for different wavelengths

Table 12.11. Values of λ T for visible boundaries

Table 12.12. Fractions f01 and f02 for each source

Table 12.13. Values of λ T for infrared band boundaries

Table 12.14. Fractions f01 and f02 for each source

Table 12.15. Distance from the ground

Table 12.16. Angle factors for different distances

Table 12.17. F12 for different values of c

Table 12.18. Values of parameter a

Table 12.19. F12 and F21

Table 12.20. Values of δ

Table 12.21. F12 for different gaps

Table 12.22. Values of c

Table 12.23. F12 for different widths

Table 12.24. Boundaries of F12 for different widths

Table 12.25. F32 as a function of δ

Table 12.26. F12 as a function of δ

Table 12.27. Number of filters to be used

Appendix

Table A.1. Densities for metals and alloys (in kg/m3)

Table A.2. Densities for construction materials (in kg/m3)

Table A.3. Densities according to manufacture (kg/m3)

Table A.4. Sensible heats for metals and alloys (J kg-1°C)

Table A.5. Sensible heats for certain construction materials (J kg-1°C)

Table A.6. Sensible heats of certain thermal insulation materials

Table A.7. Heat conductivities (metals and alloys)

Table A.8. Heat conductivities (construction materials)

Table A.9. Conductivities of certain thermal insulation materials

Table A.10. Physical data and mechanical properties of heat insulators

Table A.11. Density(ρ), sensible heat (Cp), thermal conductivity (λ), thermal di...

Table A.12. Density (ρ), sensible heat (Cp), thermal conductivity (λ), thermal d...

Table A.13. ω1 solutions according to the Biot number for planar, cylindrical or...

Table A.14. Coefficients of Aω1 according to the Biot number for planar, cylindr...

Table A.15. Evolution of function Γ for the first natural numbers

Table A.16. Molar composition of FLiNaK

Table A.17. Density of FLiNaK according to temperature (T is expressed in K, ρ i...

Table A.18. Viscosity of FLiNaK according to temperature (T is expressed in K, μ...

Table A.19. Viscosity of FLiNaK according to temperature (T is expressed in K, λ...

Table A.20. Physical properties of FLiNaK according to temperature

Table A.21. Molar composition of FLiBe

Table A.22. Density of FLiBe according to temperature (T is expressed in K, ρ is...

Table A.23. Physical properties of FLiBe according to temperature

Table A.24. Physical properties of KMgCl according to temperature

Table A.25. Molar composition of NaNOK

Table A.26. Thermal conductivities of NaNOK

Table A.27. Physical properties of NaNOK according to temperature

Table A.28. Emissivities

Table A.29. Values of f0λ for different values of λT

Table A.30. Unit conversion table

Table A.31. Fundamental constant values

Guide

Cover

Table of Contents

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Energy Engineering Set

coordinated byAbdelhanine Benallou

Volume 4

Energy Transfers by Radiation

Abdelhanine Benallou

First published 2019 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.

Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:

ISTE Ltd27-37 St George’s RoadLondon SW19 4EUUK

www.iste.co.uk

John Wiley & Sons, Inc.111 River StreetHoboken, NJ 07030USA

www.wiley.com

© ISTE Ltd 2019

The rights of Abdelhanine Benallou to be identified as the author of this work have been asserted by him in accordance with the Copyright, Designs and Patents Act 1988.

Library of Congress Control Number: 2019932202

British Library Cataloguing-in-Publication Data

A CIP record for this book is available from the British Library

ISBN 978-1-78630-277-9

Preface

“True strength is that which radiates through knowledge”.

Antonin Artaud

Umbilical Limbo (1925)

For several years, I have cherished the wish of devoting enough time to the writing of a series of books on energy engineering. The reason is simple: for having practiced for years teaching as well as consulting in different areas ranging from energy planning to rational use of energy and renewable energies, I have always noted the lack of formal documentation in these fields to constitute a complete and coherent source of reference, both as a tool for teaching to be used by engineering professors and as a source of information summarizing, for engineering students and practicing engineers, the basic principles and the founding mechanisms of energy and mass transfers leading to calculation methods and design techniques.

But between the teaching and research tasks (first as a teaching assistant at the University of California and later as a professor at the École des mines de Rabat, Morocco) and the consulting and management endeavors conducted in the private and in the public sectors, this wish remained for more than twenty years in my long list of priorities, without having the possibility to make its way up to the top. Only providence was able to unleash the constraints and provide enough time to achieve a lifetime objective.

This led to a series consisting of nine volumes:

Volume 1

: Energy and Mass Transfers;

Volume 2

: Energy Transfers by Conduction;

Volume 3

:Energy Transfers by Convection;

Volume

4: Energy Transfers by Radiation;

Volume 5

: Mass Transfers and Physical Data Estimation;

Volume 6

: Design and Calculation of Heat Exchangers;

Volume 7:

Solar Thermal Engineering;

Volume 8

: Solar Photovoltaic Energy Engineering;

Volume 9:

Rational Energy Use Engineering.

The present book is the fourth volume of this series. It concerns the study of radiation heat transfer.

As we will see, radiation is one of the most significant modes of energy transfer. Even in outer space, this mode serves to convey solar radiation and thus provide the energy necessary for life on Earth. Closely linked to electromagnetic wave transfer, radiation obeys specific rules and equations that have numerous applications in engineering.

A series of exercises is presented at the end of this document, aimed at enabling students to implement the calculation techniques specific to radiation transfer as rapidly as possible. These exercises are designed to correspond as closely as possible to real-life situations occurring in industrial practice or everyday life.

Abdelhanine BENALLOU

March 2019

Introduction

Whilst conduction and convection both represent significant modes of heat transfer in industrial equipment, radiation can be, under certain conditions, the dominant mode. This is particularly the case for heat exchange occurring in industrial furnaces and in combustion chambers.

It is also thanks to thermal radiation that the energy emitted by the Sun propagates through different media before reaching the Earth, passing through interstellar spaces comprising the extremely diffuse gases and dust of the Milky Way, the interastral voids, and the Earth’s atmosphere.

Yet transfer by radiation is characterized by an essential specific feature that differentiates it from conduction and convection. Indeed, as we saw in Volume 1 of this series, heat transfer by radiation can occur between bodies, at a distance, even without a “support medium” to convey energy. In reality, in this energy transfer, heat can even be exchanged between surfaces separated by vacuum. Of course, radiation can also take place between surfaces separated by air or by any homogeneous or non-homogeneous medium.

This energy transfer mode can therefore occur without the need for either contact-continuity (as with conduction), or a carrier fluid (as with convection). In actual fact, this characteristic is inextricably linked to the very nature of the phenomena governing radiation heat transfer and, above all, to the very essence of radiant energy. As we will demonstrate in Chapter 1, radiant energy is essentially wave-based in nature. It is generated through the transfer of electromagnetic waves between surfaces. Given that waves transport photons, radiant energy is also corpuscular in nature.

This volume aims at analyzing in detail the basics of energy transfer by radiation, according to the perspective of determining design equations for industrial equipment such as furnaces, boiler heaters, etc. This analysis uses a set of parameters that are specific to this energy transfer mode. These parameters are presented in Chapter 2 of the present volume.

Moreover, as we will see in Chapter 3, the study of radiation of matter is greatly facilitated by the introduction of a virtual component having an ideal radiative behavior. This component is referred to as a black body, the radiation of which is entirely governed by laws such as Planck’s law, the Stefan-Boltzmann law or the Wien laws.

In reality, introducing the black body constitutes a tool enabling the studying of nonvirtual, nonideal real bodies. Indeed radiation of any real surface is studied by linking it to that of the ideal black body. This is accomplished through the introduction of a specific parameter, emissivity (Chapter 4); which is defined as the ratio between the energy radiated by a real surface at a given temperature divided by the energy which would be emitted by a black body under the same temperature.

The different parameters defined in chapters 2 to 4 make it possible to analyze radiative energy transfers between surfaces separated by a transparent medium (Chapter 5).

Moreover, radiative energy exchange between surfaces depends on the geometric positions occupied by these surfaces in space. This specific feature is taken into account using angle factors, whose practical calculation methods are covered in Chapter 6.

In practical engineering calculations, it is sometimes justified to assume that some surfaces have a black body behavior. It is in this perspective that Chapter 7 is reserved for energy balances for radiations between black surfaces.

It is necessary however, to underline that the “black body assumption” does not hold for all surfaces. Those surfaces which cannot be assumed to be black are called gray surfaces. Radiative energy balances between gray surfaces represent therefore most of the practical situations encountered in engineering calculations. These cases are analyzed in Chapter 8.

From a computational point of view, radiative energy balances often lead to large systems of equations to be resolved. This can be rather complicated when more than two surfaces are involved. But the introduction of electrical analogs (see Chapter 9) can lead to easier ways of resolution.

In most practical situations, we wish to maximize energy transfer between surfaces. But in certain cases, we may wish to reduce the transfers by radiation between surfaces. This is for example the case when you try to reduce energy input to a building from its glazing. This task is generally accomplished by introducing filters. Chapter 10 shows that interposing filters between surfaces can lead to significant reductions in the energy exchanged.

On a different note, in furnaces and boilers we often encounter energy transfer by radiation between surfaces which are separated by non-transparent media. Indeed, the latter are often charged with molecules of carbon dioxide (CO2), water vapor (H2O) and traces of SO2, NOx and unburned hydrocarbons. Under these conditions (see Chapter 11), the medium contributes to the exchange by absorbing a portion of the radiation and by reflecting another portion.

Lastly, in order to help the reader assimilate the calculation methods presented in this book, Chapter 12 is devoted to a series of practical exercises and to the presentation of their solutions; meanwhile the physical data required for the calculations are grouped together in the Appendix (database).

1Origin of Radiation

1.1. Introduction

The origin of radiation is almost as old as the history of the creation of matter. Its essence finds itself combined with that of matter and electromagnetic waves originating far back in the Big Bang. Indeed, according to the Big Bang model, presented in the form of a light-hearted summary in a reader-friendly article (Lachiezo-Rey, 2016), the first particles (quarks) assembled to form protons and neutrons. Then, this assembly process continued to form the first atomic nuclei. This is known as primordial nucleosynthesis.

It enabled the development of the simplest atomic nuclei: hydrogen (1 proton), deuterium (proton + 1 neutron), helium (2 protons + 2 neutrons) and lithium (3 protons and 4 neutrons). All other nuclei known to us today as constituting matter would be formed later.

In ionized gas state, this matter emits electromagnetic waves that will be received by the rest of the matter. These energy exchanges between matter and electromagnetic waves form the basis of processes that allowed other nuclei to develop, resulting in the composition of matter that we know today.

The origin of radiation is thus found confined in infinitesimal matter.

The work conducted by Max Planck (1858–1947), Niels Bohr (1885–1962) and Albert Einstein offers a model that allows us to trace back to the corpuscular origin of radiation. Indeed, interactions between radiation and matter, first demonstrated by Max Planck, showed that exchanges between electromagnetic radiation and matter can only occur in bundles, having specific energies that depend on the matter considered. He referred to these bundles as quanta and so quantum mechanics was born.

Albert Einstein would later conclude that these quanta are carried by particles: photons. He also asserted that these photons move at the speed of light and that they convey energy which is characterized by a wave of length λ, well defined by the matter considered.

Niels Bohr’s atomic model came to complete this representation of radiation-matter interactions.

1.2. The Niels Bohr model

In Bohr’s model, an atom can only exist in certain energy states. Each of these states is defined by a specifically-determined energy level. The transition from an initial state, defined by energy level Ei, to a final state (EF) can only take place with a radiation of energy ER, such that:

Thus (see Figure 1.1), the transition of an atom from an excited state (EE) to a less excited state (EM) leads to the emission of a photon, the energy (hν) of which is such that:

Figure 1.1.Radiation emission by de-excitation of an atom. For a color version of this figure, see www.iste.co.uk/benallou/energy4.zip

Conversely, the absorption of a photon of energy hν by an atom that is at initial energy level, Ei, returns it to an excited state, EE, such that (see Figure 1.2):

Figure 1.2.Excitation of an atom by absorption of a photon. For a color version of this figure, see www.iste.co.uk/benallou/energy4.zip

Thus, the quantum model shows that:

– When matter is subject to electromagnetic radiation (such as solar radiation), and when the radiation wavelength corresponds to the absorbable quanta, then the matter can be excited. Absorption of this energy by the matter induces a switching to a more excited state. On an atomic scale, the latter can be reflected by a change in the matter energy level. Yet, on the scale of several atoms grouped into a molecule, excitation is reflected by vibrations-translations of the atoms making up the molecular structure, thus leading to an increase in the matter temperature.

– Conversely, when the matter is in an excited state (due to heating or electrical discharge, for example), and when this matter can exist in a lower energy level, then the energy of the excited state can decay, generating a quantum, the wavelength of which is compatible with the lower energy levels of the matter considered. In other words, the matter can emit electromagnetic radiation by placing itself at a more stable energy level.

The following illustrations demonstrate the different applications of this phenomenon, which enable heating and the generation of lighting for example.

1.2.1. Illustration: excitation of the neon atom

Neon tubes are used in illuminated signs. They usually contain neon in the form of low-pressure gas. The tubes generally comprise two electrodes, one on each edge.

When energized, these electrodes generate a potential difference that results in the circulation of electrons within the gas. The electrons then transfer energy to the neon atoms, placing them in a higher energy state. Then, as they de-excite, the neon atoms emit a red light.

Figure 1.3 represents the different energy sta es of the neon atom.

Figure 1.3.Energy states of the neon atom (in eV)

Questions