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.