Radiative transfer in absorbing, emitting and isotropically scattering segregated two-layered, 3D rectangular enclosures

- The radiative transfer equation in 3-D two-layer segregated media is derived.
- The exact integral transfer equations are solved numerically using Newton-Cotes quadratures.
- The medium scattering albedos and the extinction coefficients' ratio are varied.
- Five-significant-figure accurate solutions are in tabular forms provided for benchmarking purposes.

The exact 3-D radiative integral transfer equations (RITEs) for a rectangular absorbing, emitting and isotropically scattering, vertically segregated two-layered media are solved. The subtraction of singularity technique is used to handle singularities and to obtain the numerical solution of the RITEs. The surface and the volume integrals that arise in this method are evaluated analytically to handle the singular integrals and to reduce computational time. The enclosure is composed of two vertically-stacked layers in which the medium properties are discontinuous at the interface. The numerical integrations are carried out using sixth order Newton-Cotes quadratures along with the composite rule which assures highly accurate integration. In the numerical simulations, the optical thickness of layer-1 (τzp=0.25, 0.5, 0.75 mfp) and the medium properties of both layers are varied over a wide range, and the net partial radiative heat fluxes and the incident energy distributions are obtained along the vertical centerline and specified boundary lines of the enclosures for the extinction ratios of βr=0.25 and 4. For selected enclosures and medium, five-significant-digit accurate exact solutions for the incident energy and the partial heat fluxes are also provided in tabular forms for benchmarking purposes.