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.

1 Introduction.- 1.1 Thermal Radiation.- 1.2 Short Historical Background.- 1.3 Motivations, Objectives and Scope.- 1.4 Basic Concepts in Boundary Value Problems.- 2 Physical Model.- 2.1 Emitted Radiation.- 2.2 Incident, Absorbed and Scattered Radiation.- 2.3 Radiation from Particulate Matter.- 2.4 Governing Equations with Shadow Zones.- 2.5 Energy Balance Relations.- 2.6 Energy Balance on a Unit Surface.- 3 Some Computational Methods.- 3.1 Directional Equation Methods.- 3.2 Net Energy Balance 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.- 5.5 Convergence of the Numerical Solution.- 5.6 Definition of Shape Functions.- 5.7 Quadrature for the Coefficients of B and L.- 5.8 Algorithm for Computer Realization.- 6 Simulations in Specific Cases.- 6.1 The Transparent Medium.- 6.2 The Isothermal Gray Medium.- 6.3 The Non-isothermal Gray Medium.- 6.4 Non Gray Medium; Band Approximation.- 7 Spectral Properties of Gases.- 7.1 Principle of Infrared-Radiation in Gases.- 7.2 Properties of an Isothermal Gas Species.- 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.- 8.3 Concluding Remarks.- 8.4 Photo Panels - Experimental Flames.- 8.5 In-Flame and Wall Measurements.- 9 Radiation in Scattering Media.- 9.1 Formulation of theProblem.- 9.2 Radiation Heat Transfer with Conduction and/or Convection.- 9.2.2 Concluding Remarks.- 10 Conclusion.- Nomenclature.- References.