Directional spectral emittance of an absorbing and scattering isothermal system of packed spheres is predicted by a radiative model based on the discrete ordinates method. Radiative properties for the bed of packed opaque spheres are obtained using geometric optics laws corrected with a scaling factor to take into account the dependent scattering. This model requires the knowledge of several parameters. Particle diameter and porosity can be easily obtained, but particle hemispherical spectral reflectivity is very difficult to obtain a priori. This particle reflectivity is determined by an identification method (Gauss method of linearization) applied to bidirectional spectral reflectance data obtained from an experimental device using a Fourier transform infrared spectrometer. Directional spectral emittance is measured using a direct radiometric technique that has been recently proposed. For a system of packed opaque spheres at high temperature, good agreement is observed between experimental results of directional spectral and computed theoretical data.
Recently a new experimental set-up for measuring the directional spectral emittance has been developed. Both sides of packed opaque spheres are simultaneously heated with identical power laser beams (CO2 10.6 μm) and the isothermal condition in the medium is assumed. In this paper we consider the coupled conduction-radiation equations to investigate the effect of the temperature nonuniformity on the calculated value of the emittance and to verify if the isothermal assumption is valid. Moreover, the sensitivity of the emittance and the temperature profile to the values of parameters (such as the porosity, the face temperatures, and the particle hemispherical reflectivity, etc.) is studied.
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