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- Herausgeber: John Wiley & Sons
- Kategorie: Fachliteratur
- Sprache: Englisch
Heat is a branch of thermodynamics that occupies a unique position due to its involvement in the field of practice. Being linked to the management, transport and exchange of energy in thermal form, it impacts all aspects of human life and activity.
Heat transfers are, by nature, classified as conduction, convection (which inserts conduction into fluid mechanics) and radiation. The importance of these three transfer methods has resulted justifiably in a separate volume being afforded to each of them. This second volume is dedicated to radiation. After recalling photometry, the calculation of luminance is addressed using the theory of the black body and associated laws: Stefan, Wien. The reciprocal radiation of two surfaces in total influence is discussed extensively, and the case of finished surfaces is also considered.
Heat Transfer 2 combines a basic approach with a deeper understanding of the discipline and will therefore appeal to a wide audience, from technician to engineer, from doctoral student to teacher-researcher.
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Veröffentlichungsjahr: 2021
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Table of Contents
Cover
Title Page
Copyright
Preface
Introduction
I.1. Preamble
I.2. Introduction
I.3. Interlude
1 General Remarks
1.1. Introduction
1.2. Propagation of a sinusoidal electromagnetic wave
1.3. The concept of photometry
2 Calculating Luminances
2.1. Introduction
2.2. The black body: concept, luminance, Planck’s law and approximations
2.3. Stefan–Boltzmann law
2.4. Wien’s laws
2.5. Fraction of the total emittance of a black body radiated in a spectral band
2.6. Emissivity of any body: a general case of a non-black body
2.7. Simple applications
3 Emission and Absorption
3.1. Introduction
3.2. Absorption, reflection, transmission
3.3. Kirchhoff’s law
3.4. Recap on the global absorption coefficient
3.5. General case: multiple transfers
3.6. Absorption: the Beer–Lambert law
4 Radiation Exchanges Between Surfaces
4.1. Introduction
4.2. Classification
4.3. The case of total influence
5 Analytic Applications
5.1. Introduction
5.2. Radiators, convectors and radiating fins
5.3. Radiation and oven
5.4. Radiation and metrology
5.5. General problems
6 Modeling and Simulations under ANSYS
6.1. Conduction, convection and radiation
6.2. Conduction and convection using ANSYS software
6.3. Radiation using ANSYS software
6.4. Examples of modeling and analysis with ANSYS
6.5. Study of a thermal exchanger on ANSYS
6.6. Conclusion
Appendix: G0−λT Function Table
References
Index
End User License Agreement
List of Tables
Chapter 4
Table 4.1. Comparison of (1 + ε)
n
and of its approximate expression 1 + nε
Chapter 6
Table 6.1. Parameters and associated values
Table 6.2. Thermo-physical properties of hydrated salt
Table 6.3. Thermo-physical properties of paraffin
List of Illustrations
Chapter 1
Figure 1.1. Concept of the solid angle. For a color version of this figure, see ...
Figure 1.2. Illustration of . For a color version of this figure, see www.iste....
Figure 1.3. The angle θ, For a color version of this figure, see www.iste.co.uk/...
Chapter 2
Figure 2.1. General appearance of the luminance of the black body, at some tem...
Figure 2.2. Comparison of the exact luminance of the body with both approximat...
Figure 2.3. Luminances compared for the Sun and the Earth, considered as a black...
Figure 2.4. Principle of radiative forcing. For a color version of this figure, ...
Chapter 3
Figure 3.1. Schematic of radiative exchanges at a surface. For a color version o...
Chapter 4
Figure 4.1. Example of radiation between multiple surfaces
Figure 4.2. The two plate models
Chapter 5
Figure 5.1. Emissivity from the plate. For a color version of this figure, see w...
Figure 5.2. Influence of the emissivity on the emittance from the plate. For a c...
Figure 5.3. Real emittance from the plate according to the wavelength. The maxim...
Figure 5.4. Device for measuring thermal conductibility. First time: no error so...
Figure 5.5. Device for measuring thermal conductibility a second time. An initia...
Figure 5.6. Device for measuring thermal conductibility. Third time: a second so...
Figure 5.7. Fahrenheit 451, I
Figure 5.8. Fahrenheit 451, II
Chapter 6
Figure 6.1. Schematic of conduction in a tube
Figure 6.2. Three types of thermal transfer summarized using a casserole
Figure 6.3. Procedure to use with ANSYS
Figure 6.4. Study model with different boundary conditions
Figure 6.5. Model, built and meshed
Figure 6.6. Model under boundary conditions
Figure 6.7. Result from the model showing the effect of simple conduction
Figure 6.8. shows our model in ANSYS, meshed and fully defined.
Figure 6.9. Model using ANSYS with loads and conditions
Figure 6.10. Result of mixing conditions (convection/conduction/isolation)
Figure 6.11. Transistor
Figure 6.12. Results of the temperature evolving at the initial state
Figure 6.13. Results of the temperature evolving after 30 seconds
Figure 6.14. Results of the temperature evolving after 60 seconds
Figure 6.15. Results of the temperature evolving after 105 seconds
Figure 6.16. Results of the temperature evolving after 240 seconds
Figure 6.17. Results of the temperature evolving at the end of our study (T=300 ...
Figure 6.18. Evolution of the temperature according to time for the central node...
Figure 6.19. Model for the thermal study
Figure 6.20. Geometry of our meshed model
Figure 6.21. Model under loads
Figure 6.22. Temperature distribution in the oven
Figure 6.23. Thermal fluxes present in the walls of the oven
Figure 6.24. Graph representing the variation in temperature according to the se...
Figure 6.25. Geometry studied: a reservoir intersected by a tube
Figure 6.26. Quarter geometry
Figure 6.27. Meshed geometry with a fine mesh (level size = 1)
Figure 6.28. Modeling loads on our model (with arrows)
Figure 6.29. Temperature distribution in our system
Figure 6.30. Distribution of heat flux vectors at the intersection between the r...
Figure 6.31. Construction of the cylinder on a 3D model using ANSYS Workbench
Figure 6.32. Mesh of the cylinder
Figure 6.33. Application of the study conditions on the cylinder
Figure 6.34. Results of temperatures in stationary thermics on the cylinder
Figure 6.35. Results of the directional heat fluxes in thermal stationary on the...
Figure 6.36. Construction of a puck on a 3D model from ANSYS Workbench. The view...
Figure 6.37. Applying convection on the puck
Figure 6.38. Results in transitory thermal obtained on the puck after 30 seconds
Figure 6.39. Results in transitory thermal obtained on the puck after 10,000 sec...
Figure 6.40. Temperature results in thermal transitory on the thermal exchanger
Figure 6.41. Results of heat flux in thermal transitory on the thermal exchanger
Figure 6.42. Parameterizing of a heat flux to simulate the heat extricated by an...
Figure 6.43. Parameterizing a convection
Figure 6.44. Parameterizing the radiation
Figure 6.45. Development of a mesh with ANSYS Workbench
Figure 6.46. Temperature versus time for a simulation without a PCM
Figure 6.47. Temperature results for the hydrated PCM salt with a heat flux of 1...
Figure 6.48. Representation of heat on the thermal exchanger (seen from below)
Figure 6.49. Representation of heat on the thermal exchanger seen from above)
Figure 6.50. Temperature results for paraffin as a MCP with a heat flux of 1,200...
Figure 6.51. Graphical representation of the different heat fluxes applied for h...
Figure 6.52. Graphical representation of the different heat fluxes applied for p...
Figure 6.53. Comparison of the three models
Guide
Cover
Table of Contents
Title Page
Copyright
Preface
Introduction
Begin Reading
Appendix: G0−λT Function Table
References
Index
End User License Agreement
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Mathematical and Mechanical Engineering Set
coordinated by
Abdelkhalak El Hami
Volume 10
Heat Transfer 2
Radiative Transfer
Michel Ledoux
Abdelkhalak El Hami
First published 2021 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 Ltd
27-37 St George’s Road
London SW19 4EU
UK
www.iste.co.uk
John Wiley & Sons, Inc.
111 River Street
Hoboken, NJ 07030
USA
www.wiley.com
© ISTE Ltd 2021
The rights of Michel Ledoux and Abdelkhalak El Hami to be identified as the authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988.
Library of Congress Control Number: 2020949611
British Library Cataloguing-in-Publication Data
A CIP record for this book is available from the British Library
ISBN 978-1-78630-517-6
Preface
Thermal science is to thermodynamics as decree is to law. It answers the following question – which all good leaders must (or should) ask themselves whenever they have an “idea”: “How would this work in practice?”. In a way, thermal science “implements” thermodynamics, of which it is a branch. A thermodynamics specialist is a kind of energy economist. Applying the first principle, they create a “grocery store”. With the second principle, they talk about the quality of their products. I add or remove heat from a source or work from a system. And the temperature, among other things, defines the quality of the energy for me.
But by what means do I take or do I give? Even calculations of elementary reversible transformations do not tell us by what process heat passes from a source to a system.
Thermal science specifies how, but “evacuates” work. If in a given problem related to, for example, a convector where an electrical energy (therefore in the “work” category) appears, it is immediately dissipated into heat by the Joule effect.
Three heat transfer modes can be identified: conduction and radiation – which can be seen separately, although they are often paired up – and convection, which is by nature an interaction of fluid mechanics and conduction.
Dividing the study of thermal science into three is the result of logic. Presenting this work in three volumes is somewhat arbitrary; in our opinion, however, this split was necessary in order to keep the volumes in the collection a reasonable size.
This is Volume 2 of a collection of problems on thermal transfer, dedicated to radiation and digital approaches to transfer. Even though it is primarily a collection of exercises, a great deal of attention is focused on lessons. For the most part, the work is a first introduction to the thermal calculation of practical devices, which may be enough in itself. For subsequent calculations, the reader will still have to turn to specialist works or encyclopedias available in the field of thermics.
In Chapter 1, after a brief historical background, we summarize the vital notions of electromagnetic radiation and how they are written. The emphasis in this book is on the aspect of energy: the notions of photometry prove indispensable at this stage of exploration.
At the heart of studying radiation, Chapter 2 focuses on calculating luminances, relying on black body laws (Planck’s law; Rayleigh–Jeans and Wien approximations) and its derivatives: Stefan–Boltzmann laws and Wien laws. For evaluating a fraction of total emittance radiated in a spectral band, the function proves vital.
Chapter 3 tackles these interactions between a light flux and a material medium, a fundamental subject in any practical calculation of radiation: the phenomena of emission, absorption, transmission, etc., as well as the Kirchhoff law, emissivity, absorption coefficient, etc.
Chapter 4 presents the general notions on reciprocal radiation from several surfaces. We distinguish total influence and reciprocal radiation from finite surfaces. This subject is central in particular to the calculation of ovens. Here, we should restrict ourselves to notions, returning to specialist works for application by professionals working with ovens.
Solving a radiation problem often involves knowing and understanding the essence of the corresponding lessons. It is therefore not so easy to produce (interesting) problems that are limited to only being a paragraph long. This is why we were led to focus in Chapter 5 on the essence of exercises dedicated to radiation and coupled transfers.
In a domain where digital methods are becoming the rule for complex situations, it seems important to reserve a particular place for “monitoring” analytical approaches. In addition to their usefulness in understanding this domain, they offer the reader a precious tool for making calculations “on the back of an envelope”.
Finally, Chapter 6 introduces the reader to a digital approach for different transfer modes. The general problem of modeling is tackled here and examples of processing using ANSYS are presented.
The Appendix covers the tabulations of GO−λT functions whose practical importance emerges from the problems.
December 2020
Introduction
I.1. Preamble
Thermal energy was probably first perceived (if not identified) by humanity, through the Sun. The themes of night and day are found at the center of most ancient myths. Humanity’s greatest fear was probably that the Sun would not return again in the morning. Fire became controlled in approximately 400,000 BP. Thermal transfer was therefore a companion of Homo ergaster, long before Homo sapiens sapiens.
However, it took a few hundred thousand years before so-called “modern” science was born. Newtonian mechanics dates from three centuries ago. Paradoxically, another century and a half passed by before energy was correctly perceived by scientists, in terms of the new field of thermodynamics. Furthermore, a systematic study of heat transfer mechanisms was carried out at the end of the 19th century, and even later for the study of limit layers, the basis of convection.
Heating, lighting and operating the steam engines of the 19th century were all very prosaic concerns. Yet this is where revolutions in the history of physics began: the explosion of statistical thermodynamics driven by Boltzmann’s genius, and quantum mechanics erupted with Planck, again with Boltzmann’s invovlement.
Advances in radiation science, particularly in sensor technology, has enabled us to push back our “vision” of the universe by a considerable number of light years. To these advances we owe, in particular, the renewed interest in general relativity that quantum mechanics had slightly eclipsed, through demonstration of black holes, the physics of which may still hold further surprises for us.
Closer to home, fundamental thermal science, whether it is conduction, convection or radiation, contributes to the improvement of our daily lives. This is particularly true in the field of housing where it contributes, under pressure from environmental questions, to the evolution of new concepts such as the active house.
The physics that we describe in this way, and to which we will perhaps introduce some readers, is therefore related both to the pinnacles of knowledge and the banality of our daily lives. Modestly, we will place our ambition in this latter area.
There are numerous heat transfer textbooks in different formats: “handbooks” attempting to be exhaustive are an irreplaceable collection of correlations. High-level courses, at universities or engineering schools, are also quite exhaustive, but they remain demanding for the listener or the reader. Specialist, more empirical thematic manuals are still focused on specialists in spite of all this.
So why do we need another book?
The authors have taught at university level and in prestigious French engineering schools, and have been involved in the training of engineers on block-release courses. This last method of teaching, which has been gaining popularity in recent years, particularly in Europe, incorporates a distinctive feature from an educational point of view. Its practice has, in part, inspired this book.
The aim is to help learners who have not had high-level mathematical training in their first years following the French Baccalaureate (therefore accessible to apprentices), and pupils with more traditional profiles. At the same time, we would like to show this broad audience the very new possibilities in the field of digital processing of complex problems.
When a miner wants to detach a block of coal or precious mineral from a wall, they pick up a pneumatic drill. If we want to construct a tunnel, we must use dynamite. The same is true for physicists.
Whether they are researchers, engineers or simply teachers, scientists have two tools in their hands: a calculator and a computer (with very variable power). Since both authors are teacher researchers, they know they owe everything to the invention of the computer. From the point of view of teaching, however, each one of the two authors has remained specialist, one holding out for the calculator and “back-of-the-napkin” calculations, and the other one using digital calculations.
The revolution that digital tools has generated in the world of “science” and “technical” fields, aside from the context of our daily lives, no longer needs to be proved. We are a “has been” nowadays if we do not talk about Industry 4.0. The “digital divide” is bigger than the social divide, unless it is part of it …
Indeed, the memory of this revolution is now fading. Have students today ever had a “slide rule” in their hands? Do they even know what it is? Yet, all the physicists behind the laws of thermal science had only this tool in hand, giving three significant figures (four with good visibility and tenacity), leaving the user to find the power of ten of the result. It goes without saying that a simple calculation of a reversible adiabatic expansion became an ordeal, which played a part in degrading the already negative image of thermodynamics held by the average student.
This reminder will seem useless to some; slide rules are at best sleeping in drawers. But there is a moral to this story: no matter what type of keyboard we type on, a calculator or a computer, our head must have control over our fingers. This book has been written on the basis of this moral.
A good physicist must have a perfect understanding of the idea of an “order of magnitude”. For this, the tool is a calculator. We always do a rough sizing of a project before moving on to detailed modeling and numerical calculations.
The two authors belong to the world of engineering sciences, meaning most of their PhD students have entered the private sector. One of them, having moved into the aerospace sector, came back to see us very surprised by the recurrence of “back-of-the-napkin” calculations in his day-to-day work.
Fundamental or “basic physics” concepts are taken from a type of manual that is resolutely different from those dedicated to the numerical approach. In this case, the authors allow themselves to believe that it is no bad thing to collect them all together in a single book, for once. This is a significant difference that will surprise some and, without doubt, be criticized by others. Nevertheless, when reading this book, an “average” student will be initiated to a field that teaching models generally promised “for later on” (or never if he/she never goes beyond a certain level of education). It is also true that fully immersed in equations and complex calculations, specialist readers will be able to “be refreshed” when faced with the short exercises, which can sometimes surprise and encourage them – why not – to go back to their roots (assuming they had indeed been there).
Another significant difference is that this book is directed at a large scientific audience, which covers possibly the entire field: researchers, PhD students or those who have obtained Confirmation and are just starting out in the field, technicians, students or professionals, engineers. This last type of scientist is perhaps the main target of this book.
So, what is this book for?
Above all, it contains problems to be worked on, of which most are accessible to all, from the level of an apprentice technician upwards, either one or two years after the Baccalaureate. This book was written in France, where scientific teaching is structured around universities, engineering Grandes Écoles, engineering training through apprenticeships and two types of technician training sections at high schools or universities. In countries with simpler models, readers should also find it useful.
It seems necessary to surround these problems with strong reminders of past learning, so that the reader does not need to permanently refer back to their manuals. We see two advantages in this: a presentation of the scientific material focusing on the problems, and a second chance for readers to integrate notions that perhaps had not been well understood in the initial teaching.
Lastly, upon rereading, the authors also recommend this book as an introduction to the taught disciplines.
I.2. Introduction
Thermal science is to thermodynamics as decree means is to law. It answers the following question – which all good leaders must (or should) ask themselves whenever they have an “idea”: “How would this work in practice?”.
In a way, thermal science “implements” thermodynamics, of which it is a branch.
A thermodynamics specialist is a kind of energy economist. Applying the first principle, they create a “grocery store”. With the second principle, they talk about the quality of their products. I add or remove heat from a source or work from a system. And the temperature, among other things, defines the quality of the energy for me.
But by what means do I take or do I give? Even calculations of elementary reversible transformations do not tell us by what process heat passes from a source to a system.
Thermal science specifies how, but “evacuates” the work. If in a given problem related to, for example, a convector where electrical energy (therefore in the “work” category) appears, it is immediately dissipated into heat by the Joule effect.
Three heat transfer modes can be identified: conduction and radiation – which can be seen separately, although they are often paired up – and convection, which is by nature an interaction of fluid mechanics and conduction.
Dividing the study of thermal science into three volumes is the result of logic. Presenting this work in three volumes is somewhat arbitrary; in our opinion, however, this split was necessary in order to keep the volumes in the collection a reasonable size.
The first volume, entitled Heat Transfer 1, is dedicated to “classic” approaches (analytical treatment) to conduction, which will be of greater interest to readers who are looking for “simple” prediction methods.
The second volume, entitled Heat Transfer 2, is dedicated to “classic” approaches (analytical treatment) of radiation, and assembles digital approaches of these various transfer modes. It is aimed at engineers or researchers who want to resolve more complex problems.
The third volume, entitled Heat Transfer 3, is focused on convection transfers. As we have already pointed out, all of these transport operations are rarely pure and lead to problems that involve three inter-connecting transfer modes, conduction, convection and radiation.
Before our readers immerse themselves in a text that, despite our best efforts, remains intellectually demanding, we propose a short text that is a little lighter.
I.3. Interlude
Let us imagine, in a “B movie” context, a somber hostel in the gray fog of a port in the middle of nowhere. Sailors from a faraway marina come and drink away their troubles. And as always, the drink helping them along, they turn to fighting.
