Radiative transfer in arbitrarily-shaped axisymmetric enclosures with anisotropic scattering media

A two-dimensional finite volume scheme solving the axisymmetric radiative heat transfer based on general structured grids

“…The geometry of the rocket nozzle model is depicted in Fig.8. The axial temperature distributions of nozzle wall and combustion products are listed in the paper of Nunes et al (2000). The nozzle wall is gray with the emissivity of 0.8; the top boundary of the combustion chamber perpendicular to the x-axis is set to be black with the same temperature of the neighboring gas; the exiting cross-section is assumed to be gray with the emissivity of 0.8 and the temperature equal to the adjacent gas.…”

“…The combustion products are treated as the absorbing, emitting and anisotropically scattering soot/carbon particles with the uniform diameter of 30 μm and concentration N p = 5 × 10 8 par/m 3 . The radiation properties of particles are calculated by the expressions of Nunes et al (2000). Figure 9 illustrates the nondimensional radiative heat flux distribution along the nozzle wall.…”

Heat Transfer Analysis and Design for Bulk Crystal Growth: Perspectives on the Bridgman Method

“…As may be surmised from its name, this dimensionless parameter is a measure of the relative importance of conductive heat transfer with respect to radiant transport in an optically thick medium. A reasonable approach for representing internal radiation transport through such materials is called the band approximation, where the medium is assumed to exhibit a combination of transparent and opaque behaviors [79][80][81][82][83][84][85]. Therefore, a better approach is the P 1 approximation, also known as the differential and Milne-Eddington approximations [26], where a finite set of moments are employed to reduce the integral terms of the radiation transfer equation to differential terms.…”

Exact Solution of Radiative Transfer Equation for Three-Dimensional Rectangular, Linearly Scattering Medium

“…Using Eqs. (20)(21)(22) and the area elements from Table 1, Eq. (12) yields the following expression: Equations (13) and (14) are similarly treated to yield…”

“…A three-dimensional control volume finite element method for the treatment of the RTE applied to emitting, absorbing, and scattering media was developed by Grissa et al [19]. Two numerical models for solving thermal radiative transport in irregularly shaped axisymmetric geometry containing homogeneous, anisotropically scattering media were presented by Nunes et al [20].…”