Table Of ContentRadiation Heat Transfer
Modelling with
Computational Fluid
Dynamics
Radiation Heat Transfer
Modelling with
Computational Fluid
Dynamics
Yehuda Sinai
Cover image: Magnum Fire, Kaibab National Forest, USA. Reproduced from Flickr
First edition published 2022
by CRC Press
6000 Broken Sound Parkway NW, Suite 300, Boca Raton, FL 33487-2742
and by CRC Press
4 Park Square, Milton Park, Abingdon, Oxon, OX14 4RN
CRC Press is an imprint of Taylor & Francis Group, LLC
© 2022 HeatAndFlow Consultancy Limited
Reasonable efforts have been made to publish reliable data and information, but the author and publisher
cannot assume responsibility for the validity of all materials or the consequences of their use. The authors
and publishers have attempted to trace the copyright holders of all material reproduced in this publication
and apologize to copyright holders if permission to publish in this form has not been obtained. If any
copyright material has not been acknowledged please write and let us know so we may rectify in any
future reprint.
Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced,
transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter
invented, including photocopying, microfilming, and recording, or in any information storage or retrieval
system, without written permission from the publishers.
For permission to photocopy or use material electronically from this work, access www.copyright.com
or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-
750-8400. For works that are not available on CCC please contact mpkbookspermissions@tandf.co.uk
Trademark notice: Product or corporate names may be trademarks or registered trademarks and are used
only for identification and explanation without intent to infringe.
Library of Congress Cataloging-in-Publication Data
Names: Sinai, Yehuda L., author.
Title: Radiation heat transfer modelling with computational fluid dynamics/Yehuda L. Sinai.
Description: First edition. | Boca Raton : CRC Press, 2022. | Includes bibliographical references and
index. | Summary: “Radiation Heat Transfer Modelling with Computational Fluid Dynamics serves
as a reference for principles of thermal radiation and its modelling in computational fluid dynamics
(CFD) simulations. Including strategies for combining CFD and thermal radiation, the book covers
computational techniques for solving the Radiative Transfer Equation, the strengths and weaknesses
thereof, boundary and initial conditions, and relevant guidelines. Describing the strategic planning of a
typical project, it includes spectroscopic properties of gases, some particulates, and porous media. The
book is intended for researchers and professionals who simulate problems that involve fluid flow and
heat transfer with thermal radiation”-- Provided by publisher.
Identifiers: LCCN 2021050628 (print) | LCCN 2021050629 (ebook) | ISBN 9780367766115 (hardback)
| ISBN 9780367767884 (paperback) | ISBN 9781003168560 (ebook)
Subjects: LCSH: Heat--Radiation and absorption. | Heat--Transmission. | Computational fluid dynamics.
Classification: LCC TJ260 .S577 2022 (print) | LCC TJ260 (ebook) | DDC 621.402/2--dc23/eng/20211123
LC record available at https://lccn.loc.gov/2021050628
LC ebook record available at https://lccn.loc.gov/2021050629
ISBN: 978-0-367-76611-5 (hbk)
ISBN: 978-0-367-76788-4 (pbk)
ISBN: 978-1-003-16856-0 (ebk)
DOI: 10.1201/9781003168560
Typeset in Times
by SPi Technologies India Pvt Ltd (Straive)
Dedication
‘To the memory of my parents,
Dolly and Reuben.’
Contents
List of Figures ...........................................................................................................xi
List of Tables ..........................................................................................................xvii
Preface .....................................................................................................................xix
Acknowledgements .................................................................................................xxi
Disclaimer .............................................................................................................xxiii
Author ....................................................................................................................xxv
List of Symbols ....................................................................................................xxvii
Acronyms ............................................................................................................xxxiii
Chapter 1 Introduction ..........................................................................................1
Chapter 2 A Brief Outline of CFD ........................................................................7
2.1 Preliminaries ..............................................................................8
2.2 Governing Equations .................................................................9
2.3 Geometry and Meshing ...........................................................11
2.4 More Physics ...........................................................................13
2.5 Numerics ..................................................................................19
2.6 Problem Size ............................................................................20
Chapter 3 Outline of a Typical Process for CFD Analysis with Radiation .........21
Chapter 4 Fundamentals of Thermal Radiation ..................................................25
4.1 Basics .......................................................................................25
4.1.1 Electromagnetic Spectrum .........................................25
4.1.2 Black Bodies, Surface Behaviour, and Radiosity .......26
4.1.3 Speed of Light and Refractive Index ..........................32
4.1.4 Shape Factors .............................................................33
4.1.5 Introduction to the Electrical Analogy .......................34
4.1.6 Radiation Intensity .....................................................35
4.1.7 Radiative Flux ............................................................36
4.1.8 Diffusion, Anisotropy, and Collimation .....................37
4.1.9 Interfaces and Refraction ............................................40
4.1.10 Scattering ....................................................................42
4.1.11 The Meaning of ‘Incident’ and ‘Mean’ Radiation
or Intensity ..................................................................44
4.1.12 Mean Radiant Temperature ........................................45
4.2 Introduction to the Radiative Transfer Equation and Opacity .....46
4.3 Estimation of a Characteristic Opacity, and
Dimensionless Groups .............................................................50
vii
viii Contents
4.4 Coupling between Flow and Radiation ...................................52
4.4.1 Coupling between Radiation and Turbulence.............57
4.5 Equilibrium or Non-Equilibrium? ...........................................60
4.6 The Meaning of ‘Semi-Transparent’ .......................................60
4.7 Semi-Transparent Slabs, Windows, Solar Radiation ...............61
Chapter 5 Modelling ...........................................................................................65
5.1 Boundary Conditions ...............................................................65
5.1.1 Opaque Walls ..............................................................67
5.1.2 Collimated Radiation ..................................................74
5.1.3 Semi-Transparent Boundaries (Windows) .................74
5.1.4 Inlets, Outlets and Openings ......................................79
5.1.5 Symmetry Planes ........................................................79
5.2 Initial Conditions .....................................................................79
5.3 Spectroscopic Properties .........................................................79
5.3.1 Overview ....................................................................81
5.3.2 Global Models ............................................................83
5.3.2.1 Grey Models ...............................................83
5.3.2.2 Weighted Grey Gas Models (WSGG).........84
5.3.2.3 Full-Spectrum k-Distribution (FSK) ...........85
5.3.3 Band Models ..............................................................86
5.3.3.1 Wide Band Models .....................................86
5.3.3.2 Narrow-Band Models (NBM) .....................87
5.3.4 Line-by-Line Models (LBLM) ...................................87
5.3.5 Summary of Pros and Cons of the
Property Models .....................................................88
5.3.6 Porous Media ..............................................................88
5.3.7 Particulates .................................................................91
5.4 Solution Techniques ................................................................95
5.4.1 Transparent Media ......................................................95
5.4.2 Participating Media ....................................................96
5.4.2.1 Rosseland ....................................................97
5.4.2.2 Schuster–Schwarzschild .............................97
5.4.2.3 Zonal ...........................................................98
5.4.2.4 Finite Volume (FV) .....................................98
5.4.2.5 Spherical Harmonics (P ) ...........................98
N
5.4.2.6 Discrete Ordinates (S ) ...............................99
N
5.4.2.7 Discrete Transfer (DT) ................................99
5.4.2.8 Monte Carlo (MC) ......................................99
5.4.2.9 Hybrid Methods ........................................100
5.4.2.10 Scattering Capabilities ..............................101
5.4.2.11 Examples of Some Pitfalls ........................101
5.4.3 Comparisons of the RTE Solution Methods .............103
Contents ix
5.5 Estimation of Irradiation at Sub-Grid Objects in
a CFD Simulation ..................................................................105
5.6 Computational Meshes ..........................................................106
Chapter 6 Quality Assurance.............................................................................107
Chapter 7 Examples ..........................................................................................109
7.1 Utility Boiler ..........................................................................109
7.2 Forensic Investigation of a Furniture Store Fire ....................113
7.3 Sensitivity Tests of Grey Gas Models for Pool Fires .............116
7.3.1 Physical and Numerical Modelling ..........................118
7.3.2 Results and Discussion .............................................121
7.3.2.1 Closed Compartment ................................121
7.3.2.2 Open Environment ....................................121
7.3.2.3 Vented Compartment ................................121
7.3.3 Final Remarks ..........................................................123
7.4 Headlight ...............................................................................123
Appendix A: Dimensionless Groups .................................................................127
Appendix B: The Electrical Analogy ................................................................131
Appendix C: Fresnel’s Equations .........................................................................133
Appendix D: Spherical Coordinates, and More on Scattering ..........................137
Appendix E: Exact Closed-Form Solution For An Infinite, Plane, Grey,
Homogeneous, Absorbing-Emitting Slab Between Two Plates
With Different Temperatures And Emissivities ...........................139
Appendix F: Exact Closed-Form Solution For An Infinite, Plane, Grey,
Absorbing-Emitting Slab In Radiative Equilibrium Between
Two Plates With Different Temperatures And Emissivities .........143
Appendix G: The Williams Theory For An Infinite, Plane, Grey, Homogeneous,
Absorbing-Emitting, Isotropically Scattering Slab Between
Two Plates With Different Temperatures And Emissivities .........145
Appendix H: Optically Thick Limit Of The Williams Theory For A Grey,
Absorbing-Emitting And Scattering Slab ....................................147
Appendix I: Integrated Form Of The Radiative Transfer Equation .................149
Appendix J: Saturated Vapour Pressure Of Water ............................................151
Appendix K: A Steady-State 1-D Boundary Condition For Single and
Double Semi-Transparent Slabs ...................................................153
References ..........................................................................................................157
Index ....................................................................................................................173
