Nonisothermal Nongray Absorbing-Emitting-Scattering Suspension of Fe3O4 Particles Under Concentrated Solar Irradiation

Abstract

Radiation transfer within a cloud of magnetite (Fe3O4) particles contained in an infinite slab is considered. The particulate cloud is modeled as a pseudo-continuous, nongray, nonisothermal, absorbing, emitting, and anisotropically scattering medium. The energy source is concentrated solar irradiation, which is assumed to be diffusely and uniformly distributed over a circular opening and has a 5780 K blackbody spectrum. Mie-scattering theory is applied to calculate the spectrally and directionally dependent optical properties of the particles. The Monte Carlo ray-tracing method is used to calculate the attenuation characteristics of the cloud and the temperature distribution under radiative equilibrium. The Monte Carlo simulation is optimized by incorporating the appropriate cumulative probability density functions via Bezier surfaces. The effect of spectral and directional dependency is investigated by comparing the results with those obtained for a gray and isotropic-scattering medium under diffuse or perpendicular incident radiation. It is found that a cloud of Mie-scattering Fe3O4 particles under perpendicular incident radiation requires approximately twice as much optical thickness to obtain the same attenuation (of radiation at all wavelengths and directions) as a cloud of isotropic-scattering particles under diffuse incident radiation. It is demonstrated that the gray approximation using Planck mean values can lead to considerable error in the temperature solution because the spectral absorption coefficient is higher in the region of longer wavelengths where the peak emission by Fe3O4 particles occurs.