Cover
Series Preface
Preface
Acknowledgments
About the Companion Website
1 Fundamentals of Ray Tracing
1. 1.1 Rays and Ray Segments
2. 1.2 The Enclosure
3. 1.3 Mathematical Preliminaries
4. 1.4 Ideal Models for Emission, Reflection, and Absorption of Rays
5. 1.5 Scattering and Refraction
6. 1.6 Meshing and Indexing
7. Problems
8. Reference
2 Fundamentals of Thermal Radiation
1. 2.1 Thermal Radiation
2. 2.2 Terminology
3. 2.3 Intensity of Radiation (Radiance)
4. 2.4 Directional Spectral Emissive Power
5. 2.5 Hemispherical Spectral Emissive Power
6. 2.6 Hemispherical Total Emissive Power
7. 2.7 The Blackbody Radiation Distribution Function
8. 2.8 Blackbody Properties
9. 2.9 Emission and Absorption Mechanisms
10. 2.10 Definition of Models for Emission, Absorption, and Reflection
11. 2.11 Introduction to the Radiation Behavior of Surfaces
12. 2.12 Radiation Behavior of Surfaces Composed of Electrical Non‐Conductors (Dielectrics)
13. 2.13 Radiation Behavior of Surfaces Composed of Electrical Conductors (Metals)
14. Problems
15. References
3 The Radiation Distribution Factor for Diffuse‐Specular Gray Surfaces
1. 3.1 The Monte Carlo Ray‐Trace (MCRT) Method and the Radiation Distribution Factor
2. 3.2 Properties of the Total Radiation Distribution Factor
3. 3.3 Estimation of the Distribution Factor Matrix Using the MCRT Method
4. 3.4 Binning of Rays on a Surface Element; Illustrative Example
5. 3.5 Case Study: Thermal and Optical Analysis of a Radiometric Instrument
6. 3.6 Use of Radiation Distribution Factors for the Case of Specified Surface Temperatures
7. 3.7 Use of Radiation Distribution Factors When Some Surface Net Heat Fluxes Are Specified
8. Problems
9. Reference
4 Extension of the MCRT Method to Non‐Diffuse, Non‐Gray Enclosures
1. 4.1 Bidirectional Spectral Surfaces
2. 4.2 Principles Underlying a Practical Bidirectional Reflection Model
3. 4.3 First Example: A Highly Absorptive Surface Whose Reflectivity is Strongly Specular
4. 4.4 Second Example: A Highly Reflective Surface Whose Reflectivity is Strongly Diffuse
5. 4.5 The Band‐Averaged Spectral Radiation Distribution Factor
6. 4.6 Use of the Band‐Averaged Spectral Radiation Distribution Factor for the Case of Specified Surface Temperatures
7. 4.7 Use of the Band‐Averaged Spectral Radiation Distribution Factor for the Case of One or More Specified Surface Net Heat Fluxes
8. Problems
9. References
5 The MCRT Method for Participating Media
1. 5.1 Radiation in a Participating Medium
2. 5.2 Example: The Absorption Filter
3. 5.3 Ray Tracing in a Participating Medium
4. 5.4 Estimating the Radiation Distribution Factors in Participating Media
5. 5.5 Using the Radiation Distribution Factors When All Temperatures are Specified
6. 5.6 Using the Radiation Distribution Factors for a Mixture of Specified Temperatures and Specified Heat Transfer Rates
7. 5.7 Simulating Infrared Images
8. Problems
9. References
6 Extension of the MCRT Method to Physical Optics
1. 6.1 Some Ideas from Physical Optics
2. 6.2 Geometrical Versus Physical Optics
3. 6.3 Anatomy of a Ray Suitable for Physical Optics Applications
4. 6.4 Modeling of Polarization Effects: A Case Study
5. 6.5 Diffraction and Interference Effects: A Case Study
6. 6.6 Monte Carlo Ray‐Trace Diffraction Based on the Huygens–Fresnel Principle
7. Problems
8. References
7 Statistical Estimation of Uncertainty in the MCRT Method
1. 7.1 Statement of the Problem
2. 7.2 Statistical Inference
3. Example Problem 7.1
4. 7.3 Hypothesis Testing for Population Means
5. Example Problem 7.2
6. 7.4 Confidence Intervals for Population Proportions
7. 7.5 Effects of Uncertainties in the Enclosure Geometry and Surface Models
8. 7.6 Single‐Sample Versus Multiple‐Sample Experiments
9. 7.7 Evaluation of Aggravated Uncertainty
10. 7.8 Uncertainty in Temperature and Heat Transfer Results
11. 7.9 Application to the Case of Specified Surface Temperatures
12. 7.10 Experimental Design of MCRT Algorithms
13. Problems
14. References
A
1. A.1 Pseudo‐Random Number Generators
2. A.2 Properties of a “Good” Pseudo‐Random Number Generator
3. A.3. A “Minimal Standard” Pseudo‐Random Number Generator
4. A.4 Autoregression Analysis
5. Problems
6. References
Index
End User License Agreement

List of Tables

Chapter 01
1. Table A.1 Vertical displacement observed and predicted from a third‐order autoregression model based on n + N + 1 = 7 observations (α ₁ = 2.9885, α ₂ = −2.9591, α ₃ = 0.9553).
Chapter 01
1. Table 1.1 Quadratic surfaces commonly encountered in radiation heat transfer and applied optics modeling.
Chapter 02
1. Table 2.1 Data from Dulong and Petit [13] used by Stefan [2] to establish the absolute‐temperature‐to‐the‐fourth‐power dependence of radiant heat emission from a solid body.
Chapter 03
1. Table 3.1 Radiation distribution factors from the telescope surfaces to the detector.
Chapter 04
1. Table 4.1 Fitting parameter values for the model shown in Figure 4.4 [4].
Chapter 05
1. Table 5.1 Convergence of Eq. 5.5 when ρ _ext = 0.02, a = 0.005, and ρ _int = 0.02.
Chapter 06
1. Table 6.1 Statistical comparison of the performance of the MCRT method and the standard analytical approach for predicting measured interference fringes.
Chapter 07
1. Table 7.1 Summary of results obtained using the PRNG to obtain 10 sets of 350 random numbers each.
2. Table 7.2 Relative uncertainties of distribution factors as a function of the number of surface elements n, and the number of energy bundles traced per surface element, N, for a 95% confidence interval.

List of Illustrations

Chapter 01
1. Figure A.1 A hypothetical sampled time series representing a segment of the trajectory followed by a maneuvering aircraft.
2. Figure A.2 Illustration of the interpretation of the autoregression coefficients as slopes for a second‐order autoregression.
3. Figure A.3 Observed and predicted displacements using a third‐order autoregression model for an object dropped from rest falling under the influence of gravity in a vacuum.
Chapter 01
1. Figure 1.1 Relationships among the quantities introduced in Section 1.3.
2. Figure 1.2 Definition of a plane surface.
3. Figure 1.3 Possible disposition of three rays emitted from point P ₀.
4. Figure 1.4 Candidate rays in the interior of the hollow sphere defined by Eq. 1.12.
5. Figure 1.5 In (a) both points of intersection are forward candidates while in (b) both points of intersection are back candidates.
6. Figure 1.6 Instructing the computer to designate (x ₂, y ₂, z ₂) rather than (x ₁, y ₁, z ₁) as the point of intersection of the ray on the concave spherical sector.
7. Figure 1.7 The specular reflection model.
8. Figure 1.8 The diffuse reflection model.
9. Figure 1.9 The diffuse–specular approximation of a bidirectional reflecting surface.
10. Figure 1.10 Nomenclature for incident and reflected rays.
11. Figure 1.11 Illustration of the Snell–Descartes law of refraction.
12. Figure 1.12 A hollow, three‐dimensional rectilinear space.
13. Figure 1.13 Geometry for Problem 1.13.
14. Figure 1.14 A condensing lens formed from two intersecting spherical sectors of optical glass.
15. Figure 1.15 The wedge‐shaped cavity of Problem 1.19.
16. Figure 1.16 Geometry for Problems 1.25 and 1.26.
Chapter 02
1. Figure 2.1 A y‐polarized EM wave propagating along the x‐axis.
2. Figure 2.2 The electromagnetic spectrum.
3. Figure 2.3 Illustration of the concept of the solid angle.
4. Figure 2.4 Differential solid angle subtended by a differential spherical sector at the center of a sphere.
5. Figure 2.5 A monochromatic beam of spectral intensity i _λ(λ, ϑ, ϕ) contained within differential solid angle dΩ _s leaving a plane area element dA.
6. Figure 2.6 Radiation emitted by a surface element dA into the overlying hemispherical space.
7. Figure 2.7 Comparison of the Wien, Rayleigh–Jeans, and Planck blackbody radiation distribution functions for a blackbody at a temperature of 6000 K.
8. Figure 2.8 Directional distributions of blackbody directional (a) total intensity and (b) total emissivity.
9. Figure 2.9 The atomic potential well illustrating a bound‐bound and a free‐bound transition.
10. Figure 2.10 The emission spectrum from ionized methane [9].
11. Figure 2.11 Spectral intensity of a blackbody, a graybody, and a hypothetical real surface, all at 6000 K.
12. Figure 2.12 The directional spectral intensities at a specified wavelength, temperature, and azimuth angle for a blackbody, a diffuse surface, and a hypothetical real surface.
13. Figure 2.13 The disposition of radiation incident to a surface.
14. Figure 2.14 A monochromatic beam incident to a surface element.
15. Figure 2.15 Illustration of directional‐hemispherical spectral reflectivity.
16. Figure 2.16 Illustration of hemispherical‐directional spectral reflectivity.
17. Figure 2.17 Illustration of (bi)hemispherical spectral reflectivity.
18. Figure 2.18 Extinction of the electric component of a y‐polarized EM wave propagating in the positive‐x direction through an electrical conductor.
19. Figure 2.19 A transverse‐magnetic (TM), p‐polarized, monochromatic wave incident to a smooth plane interface between two dielectrics with n ₂ > n ₁.
20. Figure 2.20 Comparison of theory and experiment for the directional spectral emissivity of black glass (n = 1.517) at 0.546 μm.
21. Figure 2.21 Comparison of theory and experiment for the directional spectral emissivity of pure platinum (n = 5.29, k = 6.71) at 2.0 μm.
Chapter 03
1. Figure 3.1 Logic block diagram of the Monte Carlo ray‐trace method for diffuse‐specular gray enclosures.
2. Figure 3.2 A concept for remote measurement of thermal radiation.
3. Figure 3.3 Outer face of the second baffle of the collimator in Figure 3.2.
4. Figure 3.4 Kowsary's method [1] for computing the direction of a diffusely reflected ray.
5. Figure 3.5 The detector subdivided into a number of bins.
6. Figure 3.6 Matlab binning pseudo‐code.
7. Figure 3.7 Data sheet for radiometric instrument concept of Figure 3.2.
8. Figure 3.8 One hundred thousand rays converging on the focal plane at z = 58.58 mm.
9. Figure 3.9 Ray intersections with the primary mirror shown as individual dots.
10. Figure 3.10 Ray intersections with the secondary mirror shown as individual dots.
11. Figure 3.11 The paths of 1000 individual rays through the telescope.
12. Figure 3.12 Absorption of radiation on the surfaces of the collimator, on the inner edge of the primary mirror (Surface 22 in Figure 3.7), and on the focal plane.
13. Figure 3.13 Distribution of rays absorbed in the focal plane (gray dots) and on the detector (black dots).
14. Figure 3.14 Distribution of non‐optical rays in the focal plane (rays absorbed by the detector shown in black are gathered in the center).
15. Figure 3.15 Variation of detector power with angle of incidence of a collimated beam.
16. Figure 3.16 Coma produced by a collimated beam of rays incident to the instrument aperture at an angle of 5°.
17. Figure 3.17 Two‐dimensional representation of a generic enclosure made up of n surface elements.
18. Figure 3.18 Geometry for Problems 3.11–3.13.
Chapter 04
1. Figure 4.1 The areas under the two curves are about the same even though the curves themselves are different.
2. Figure 4.2 Beams of monochromatic light incident to and reflected from an area element dA.
3. Figure 4.3 Schematic representation of an apparatus for measuring the BRDF of a coupon.
4. Figure 4.4 Empirical model [4] (curves) to Prokhorov and Prokhorova data [3] (symbols).
5. Figure 4.5 Models for b _n coefficients (symbols are values from Table 4.1) [4].
6. Figure 4.6 Model for B ₄ coefficient (symbols are values from Table 4.1) [4].
7. Figure 4.7 Geometry defining v _r and v _v in Eqs. 4.14–4.16. The zenith angles ϑ _i and ϑ _v are both in the plane of incidence, and the points (x _v , y _v , z _v) and (x _r , y _r , z _r) both lie in the surface of the unit hemisphere [4].
8. Figure 4.8 Scatter diagram showing the BRDF distribution resulting when a single ray incident at 45° is split into 100 000 rays according to the four‐component model [4].
9. Figure 4.9 The variation of the directional‐hemispherical reflectivity of Z302 at λ = 10.6 µm computed using Eq. 4.18 with the four‐component model for ρ(ϑ _i, ϑ _r, ϕ _r) [4].
10. Figure 4.10 The variation of the directional absorptivity of Z302 at λ = 10.6 µm computed using Eqs. 4.17 and 4.18 with the four‐component model for ρ(ϑ _i, ϑ _r, ϕ _r) [4].
11. Figure 4.11 Power measured by the detector using the apparatus of Figure 4.3 [4].
12. Figure 4.12 An integrating sphere configured to compare the responses of two radiometers to the same quasi‐diffuse target.
13. Figure 4.13 Comparison of Eqs. 4.28–4.30 with discrete values of fitting parameters [8].
14. Figure 4.14 Comparison of BRF data from Walker [9] with two models [8].
15. Figure 4.15 Ratio of power distributed to the two radiometers as a function of wall absorptivity (note that the vertical axis does not start at zero).
16. Figure 4.16 Comparison for exact and approximate expressions for the probability P(λ) that a ray will be emitted at wavelength λ when T _i = 800 K.
17. Figure 4.17 Illustration of the half‐interval search method for finding the roots of a transcendental equation.
18. Figure 4.18 The candidate solution values T making up the genes of the original generation of the P candidate “parents.”
19. Figure 4.19 A diffuse, gray spherical enclosure (Problem 4.2).
Chapter 05
1. Figure 5.1 Overlay of several structured computational fluid dynamics (CFD) meshes of a Boeing 747.
2. Figure 5.2 Comparison of (a) measured and (b) predicted mid‐wavelength range infrared images of a Boeing 747 in flight.
3. Figure 5.3 A fused silica (silicon dioxide) absorption filter.
4. Figure 5.4 Running averages of the optical constant data reported in Ref. [3], with the ideal solar and earth‐emitted spectra included.
5. Figure 5.5 Multiple internal reflections within an absorption filter.
6. Figure 5.6 Split‐filter design for reducing long‐wavelength “leak.”
7. Figure 5.7 Distribution of absorbed earth‐emitted radiation in the fused silica filter.
8. Figure 5.8 Distribution of absorbed solar‐reflected radiation in the fused silica filter.
9. Figure 5.9 Steady‐state (left) and transient (right) temperature rise on the back face of 1.0‐mm‐thick single and split fused silica filters when subjected to earth‐emitted radiation.
10. Figure 5.10 Two‐dimensional representation of a notional three‐dimensional enclosure containing a participating medium. White space is participating medium, gray space is solid, heavy lines are surfaces, and light lines are boundaries between volume elements.
11. Figure 5.11 The initial steps for computing the distribution factors from one surface or volume element of an enclosure filled with a participating medium.
12. Figure 5.12 A ray emitted within a rectangular‐solid volume element filled with a participating medium.
13. Figure 5.13 Logic followed after comparing the values of Δs _old, s _a and s _s.
14. Figure 5.14 A typical volume element, or cell, of a rectangular solid enclosure containing a participating medium.
15. Figure 5.15 Logic following identification of the boundary as either a cell interface or a wall segment.
16. Figure 5.16 Logic flow after computing the ray direction in the new volume element.
17. Figure 5.17 Disposition of a ray incident to a surface element.
18. Figure 5.18 Illustration of a MCRT model for scattering by a semi‐transparent spherical particle with n ₂ > n ₁ and 2πr/λ > 1.
19. Figure 5.19 Scattering of unpolarized 0.55‐μm radiation by a 2.0‐μm‐diameter spherical aerosol whose complex index of refraction is 1.304 − i 0.24 × 10⁻⁶.
20. Figure 5.20 Logic flow after a scattering event.
21. Figure 5.21 Comparison of (a) measured and (b) predicted infrared images of an auxiliary power unit exhaust plume. Source: Ref. [59, reprinted with permission]. (See color plate section for the color representation of this figure)
22. Figure 5.22 Geometry illustrating simulation of the infrared image of a jet plume.
Chapter 06
1. Figure 6.1 EM radiation normally incident to a long V‐groove corresponding to three values of the Fresnel number, .
2. Figure 6.2 Anatomy of an individual enhanced ray.
3. Figure 6.3 Concept for an Earth radiation budget instrument based on a two‐dimensional off‐axis parabolic mirror.
4. Figure 6.4 Distribution of one million rays in the focal plane for off‐axis angle ϑ of (a) 10, (b) 20, and (c) 30°.
5. Figure 6.5 Reflectivity distributions for s‐ and p‐polarized monochromatic rays arriving in the focal plane for off‐axis angles ϑ of (a) 10, (b) 20 and (c) 30°.
6. Figure 6.6 Predicted interference fringe pattern in detector plane for wavelengths λ of (a) 1.0, (b) 10, and (c) 34 µm.
7. Figure 6.7 The (a) wave and (b) ray views of the Huygens principle. Source: Ref. [8, reprinted with permission].
8. Figure 6.8 The MCRT diffraction model. Source: Ref. [8, reprinted with permission].
9. Figure 6.9 Logic for defining an obliquity rule for use in the MCRT method.
10. Figure 6.10 Comparison of electric dipole and diffuse directivity patterns.
11. Figure 6.11 Sensitivity of the MCRT‐predicted fringe pattern to the number of rays traced.
12. Figure 6.12 Comparison of (top to bottom) MCRT, analytical, and experimental interference fringes produced by a 200‐µm slit illuminated by a 351‐nm laser for a range of aperture‐to‐screen distances.
13. Figure 6.13 Comparison of (top to bottom) MCRT, analytical, and experimental interference fringes produced by a 100‐µm slit illuminated by a 351‐nm laser for a range of aperture‐to‐screen distances.
14. Figure 6.14 Comparison of (a) MCRT, (b) analytical, and (c) measured interference fringes corresponding to normal illumination of a 100‐µm diameter circular aperture by a 351‐nm laser for an aperture‐to‐screen distance of 1.9 mm (F = 5.48). Source: Ref. [8, reprinted with permission]. (See color plate section for the color representation of this figure)
15. Figure 6.15 Comparison of (a) MCRT, (b) analytical, and (c) measured interference fringes corresponding to normal illumination of a 200‐µm diameter circular aperture by a 351‐nm laser for an aperture‐to‐screen distance of 7.6 mm (F = 5.48). Source: Ref. [8, reprinted with permission]. (See color plate section for the color representation of this figure)
16. Figure 6.16 Comparison of (a) MCRT, (b) analytical, and (c) measured interference fringes corresponding to normal illumination of a 400‐µm diameter circular aperture by a 351‐nm laser for an aperture‐to‐screen distance of 30.4 mm (F = 5.48). Source: Ref. [8, reprinted with permission]. (See color plate section for the color representation of this figure)
17. Figure 6.17 Schematic representation of Young's experiment.
Chapter 07
1. Figure 7.1 The normal probability distribution function showing the values of t corresponding to a given confidence interval.
2. Figure 7.2 A sample of 35 pseudo‐random numbers provided by a PRNG.
3. Figure 7.3 The normal probability distribution function showing the critical value of t for a one‐sided hypothesis test.
4. Figure 7.4 Behavior of f(N, ) defined by Eq. 7.23.
5. Figure 7.5 Variation of the mean relative uncertainty in net heat flux in an enclosure with mean fourth‐power temperature spread for a range of values of ω _D/D (ω _ε/ε = ω _T/T = 0.01).

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Library of Congress Cataloging-in-Publication Data

Names: Mahan, J. R., author.

Title: The Monte Carlo ray-trace method in radiation heat transfer and

applied optics / J. Robert Mahan.

Description: Hoboken, NJ : John Wiley & Sons, 2019. | Series: Wiley-ASME

Press series | Includes bibliographical references and index. |

Identifiers: LCCN 2018036102 (print) | LCCN 2018043872 (ebook) | ISBN

9781119518525 (Adobe PDF) | ISBN 9781119518501 (ePub) | ISBN 9781119518518

(hardcover)

Subjects: LCSH: Heat--Transmission--Mathematical models. | Monte Carlo

method. | Ray tracing algorithms.

Classification: LCC QC320 (ebook) | LCC QC320 .M358 2018 (print) | DDC

536/.201518282–dc23

LC record available at https://lccn.loc.gov/2018036102

Cover design: Wiley

Preface

This book is a stand‐alone treatment of the Monte Carlo ray‐trace (MCRT) method as it is currently practiced in the field of radiation heat transfer. While intended primarily as a textbook for use by first‐year graduate students in curricula such as mechanical and aerospace engineering, the suitability of the MCRT method as an optical modeling tool makes the content equally well suited to the needs of students and practitioners of applied optics.

Max Planck, in his seminal 1912 book The Theory of Heat Radiation, writes that when undertaking radiation heat transfer analysis

…it will be assumed that the linear dimensions of all parts of space considered, as well as the radii of curvature of all surfaces under consideration, are large compared with the wave lengths of the rays considered. With this assumption we may, without appreciable error, entirely neglect the influence of diffraction caused by the bounding surfaces, and everywhere apply the ordinary laws of reflection and refraction of light.

In other words, Planck is alerting the reader that radiation heat transfer analysis is to be based on the principles of geometrical optics rather than on the more complex principles of physical optics. The material presented in the current book extends radiation heat transfer beyond this limited view. By including principles from physical optics we are able to attack problems inaccessible to geometrical optics alone.

During most of the century following the publication of Planck's book, the version of geometrical optics used in radiation heat transfer analysis has been based on its implications rather than on the literal application of its principles. Until the emergence of the high‐speed digital computer after World War II, the ray‐by‐ray application of geometrical optics to complex geometries was simply not practical. By the dawn of the new millennium, however, rapid advances in computing power had made it possible to emit and trace a statistically significant number of rays as they were scattered, refracted, and eventually absorbed within complex enclosures consisting of thousands of surface and optically participating volume elements. In other words, accurate simulation began to displace approximate analysis as a means of describing radiation heat transfer. Today, virtually no serious radiation heat transfer calculations are performed using the antiquated “net exchange” formulation, which is based on the questionable assumptions of uniform surface heat flux and diffuse gray surfaces, and is incapable by itself of treating radiation in participating media.

The mathematical basis of ray tracing and the fundamentals of thermal radiation are presented in the first two chapters. This material prepares the ground for Chapter 3, in which the MCRT method is introduced and used to model radiant exchange among diffuse gray surfaces. After the completion of the first three chapters, the reader is already armed with the essential knowledge required to formulate realistic radiation heat transfer models for the wide range of applications typically encountered in industrial settings. The next three chapters extend the MCRT method to include radiant exchange among non‐diffuse non‐gray surfaces (Chapter 4), radiation in a participating medium (Chapter 5), and the treatment of polarization, diffraction, and interference in applied optics (Chapter 6). The additional theory required to support these latter topics is introduced as the need arises. The ease of transition from the basic material of Chapter 3 to the more advanced material of Chapters 4, 5, and 6 is remarkable. This is due to the inherent flexibility of the MCRT method itself, whose basic principles apply equally well to directional wavelength‐dependent surface models as they do to diffuse gray surface models; and whose logical structure applies equally well to radiant exchange among volume elements as it does to radiant exchange among surface elements. The treatment of polarization, diffraction, and interference using the MCRT method follows naturally after the definition of a “ray” is augmented to include its wavelength, phase, and polarization state. Finally, Chapter 7 presents a formal statistical method for assessing the uncertainty, to a stated level of confidence, of results obtained using the MCRT method.

J. Robert Mahan

Blacksburg

March 2018

Introduction to Dynamics and Control in Mechanical Engineering Systems	To	March 2016
Fundamentals of Mechanical Vibrations	Cai	May 2016
Nonlinear Regression Modeling for Engineering Applications	Rhinehart	September 2016
Modeling, Model Validation, and Enabling Design of Experiments Stress in ASME Pressure Vessels	Jawad	November 2016
Combined Cooling, Heating, and Power Systems	Shi	January 2017
The monte Carlo Ray‐trace Method in Radiation heat Transfer and Applied optics	Mahan	December 2018

Wiley‐ASME Press Series List

THE MONTE CARLO RAY-TRACE METHOD IN RADIATION HEAT TRANSFER AND APPLIED OPTICS

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Dedication

Series Preface

Preface

Acknowledgments

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