Radiation in Enclosures: Elliptic Boundary Value Problem

ISBN-13: 9783642630200 / Angielski / Miękka / 2012 / 211 str.

Aristide Mbiock;Roman Weber

Opis

During the last half century, the development and testing of prediction models of combustion chamber performance have been an ongoing task at the International Flame Research Foundation (IFRF) in IJmuiden in the Netherlands and at many other research organizations. This task has brought forth a hierarchy of more or less standard numerical models for heat transfer predictions, in particular for the prediction of radiative heat transfer. Unfortunately all the methods developed, which certainly have a good physical foundation, are based on a large number of extreme sim- plifications or uncontrolled assumptions. To date, the ever more stringent requirements for efficient production and use of energy and heat from com- bustion chambers call for prediction algorithms of higher accuracy and more detailed radiative heat transfer calculations. The driving forces behind this are advanced technology requirements, the costs of large-scale experimen- tal work, and the limitation of physical modeling. This interest is growing more acute and has increased the need for the publication of a textbook for more accurate treatment of radiative transfer in enclosures. The writing of a textbook on radiative heat transfer, however, in ad- dition to working regularly on other subjects is a rather difficult task for which some years of meditation are necessary. The book must satisfy two requirements which are not easily reconciled. From the mathematical point of view, it must be written in accordance with standards of mathemati- cal rigor and precision.

Recenzje

"The book is concerned with both the formulation and the general investigation and solution of the radiative heat transfer problem in enclosures of any geometrical shape, and for any temperature distribution and material properties. ... the book contains important advances in the radiation theory and will undoubtedly usefull for engineers and specialists in this field." (Vladimir P. Burskii, zbMATH 1139.35044, 2021)

Spis treści

1 Introduction.- 1.1 Thermal Radiation.- 1.2 Short Historical Background.- 1.3 Motivations, Objectives and Scope.- 1.3.1 Motivations and Objectives.- 1.3.2 Scope Covered.- 1.4 Basic Concepts in Boundary Value Problems.- 1.4.1 Typical Examples.- 1.4.2 Integral-Transform Techniques.- 1.4.3 Numerical Approximations.- 2 Physical Model.- 2.1 Emitted Radiation.- 2.1.1 Intensity of Emitted Radiation.- 2.1.2 Radiation from a Blackbody.- 2.2 Incident, Absorbed and Scattered Radiation.- 2.2.1 Absorption.- 2.2.2 Emission.- 2.2.3 Scattering.- 2.2.4 The Equation of Radiative Heat Transfer.- 2.2.5 Integral Form of Radiative Heat Transfer Equation.- 2.3 Radiation from Particulate Matter.- 2.4 Governing Equations with Shadow Zones.- 2.5 Energy Balance Relations.- 2.5.1 General Considerations and Boundary Conditions.- 2.6 Energy Balance on a Unit Surface.- 2.6.1 Energy Balance on a Control Volume.- 2.6.2 Definition of the Solid Angle.- 2.6.3 Radiation Pressure and Stress.- 3 Some Computational Methods.- 3.1 Directional Equation Methods.- 3.1.1 The Flux and the Discrete Ordinates Methods.- 3.1.2 The Milne-Eddington or Moment Method.- 3.1.3 The Spherical Harmonics or P N-Method.- 3.1.4 The Discrete Transfer Method.- 3.1.5 Concluding Remarks.- 3.2 Net Energy Balance Methods.- 3.2.1 Probabilistic Methods.- 3.2.2 Finite Element Methods.- 3.3 Concluding Remarks.- 3.4 The Boundary Value Equation.- 4 Mathematical Model.- 4.1 Subsidiary Conditions.- 4.2 Analysis of the Boundary Value Equation.- 4.3 Canonical Formulation.- 4.4 Irradiance Formulation.- 4.5 Analytical Form of the Solution.- 4.6 Quadratic Variational Formulation.- 4.7 Variational Solution: Existence, Uniqueness.- 4.8 Continuity of the Variational Solution.- 4.9 Question of Proper Posing Problem.- 5 Numerical Approximation.- 5.1 Description of the Method.- 5.2 Finite Element Representation.- 5.3 Definition of the Approximation Space.- 5.4 Formulation of the Approximated Problem.- 5.4.1 Solution of the Approximated Problem.- 5.5 Convergence of the Numerical Solution.- 5.6 Definition of Shape Functions.- 5.7 Quadrature for the Coefficients of B and L.- 5.7.1 Required Order of Numerical Integration.- 5.7.2 Singular Integrals of the Kernel K(r,p).- 5.7.3 Regular Integrals of the Kernel K(r,p).- 5.7.4 Quadrature for the Line Integral L(r,p).- 5.8 Algorithm for Computer Realization.- 6 Simulations in Specific Cases.- 6.1 The Transparent Medium.- 6.1.1 The Blackbody Cavity.- 6.2 The Isothermal Gray Medium.- 6.2.1 The Well-Stirred Combustion Chamber.- 6.3 The Non-isothermal Gray Medium.- 6.3.1 Radiation from Jet Flames.- 6.4 Non Gray Medium; Band Approximation.- 7 Spectral Properties of Gases.- 7.1 Principle of Infrared-Radiation in Gases.- 7.1.1 Electronic Transitions.- 7.1.2 Vibrational and Rotational Transitions.- 7.1.3 Spectral Lines of Emitted Radiation.- 7.2 Properties of an Isothermal Gas Species.- 7.2.1 Exponential Wide-Band Parameters.- 7.2.2 Average Spectral Transmissivity.- 7.2.3 Spectral Band Limits.- 7.3 Properties of a Non-isothermal Gas Species.- 7.4 Medium Containing Several Gas Species.- 7.5 Band Radiation in a Well-Stirred Chamber.- 8 Application to Industrial Furnace.- 8.1 Experimental Configuration.- 8.2 Analysis of Experimental Flames.- 8.2.1 The Non-Swirling Natural Gas Flame.- 8.2.2 The Low-Swirling Natural Gas Flame.- 8.2.3 The High-Swirling Natural Gas Flame.- 8.2.4 The Non-Swirling Propane Flame.- 8.3 Concluding Remarks.- 8.4 Photo Panels - Experimental Flames.- 8.5 In-Flame and Wall Measurements.- 9 Radiation in Scattering Media.- 9.1 Formulation of the Problem.- 9.2 Radiation Heat Transfer with Conduction and/or Convection.- 9.2.1 The Energy Conservation Relation.- 9.2.2 Concluding Remarks.- 10 Conclusion.- Nomenclature.- References.

Blurb

This graduate textbook is concerned with both the formulation and the solution of radiation heat transfer problems in enclosures. The book is essentially self-contained and includes a brief historical survey. The foundations are carefully discussed from the point of view of the exact mathematical basis of boundary value problems and their variational solutions as well as of the physical foundations. The computational methods developed by the authors are used in engineering applications. The combinaton of exact mathematical modelling with numerical skills makes this a unique textbook.